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Arithmetic properties of 3-regular partitions with distinct odd parts Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2021-01-17 V. S. Veena, S. N. Fathima
Let \(pod_3(n)\) denote the number of 3-regular partitions of n with distinct odd parts (and even parts are unrestricted). In this article, we prove an infinite family of congruences for \(pod_3(n)\) using the theory of Hecke eigenforms. We also study the divisibility properties of \(pod_3(n)\) using arithmetic properties of modular forms.
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Clifford systems, Clifford structures, and their canonical differential forms Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2020-12-08 Kai Brynne M. Boydon, Paolo Piccinni
A comparison among different constructions in \(\mathbb {H}^2 \cong {\mathbb {R}}^8\) of the quaternionic 4-form \(\Phi _{\text {Sp}(2)\text {Sp}(1)}\) and of the Cayley calibration \(\Phi _{\text {Spin}(7)}\) shows that one can start for them from the same collections of “Kähler 2-forms”, entering both in quaternion Kähler and in \(\text {Spin}(7)\) geometry. This comparison relates with the notions
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A counting invariant for maps into spheres and for zero loci of sections of vector bundles Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2020-11-27 Panagiotis Konstantis
The set of unrestricted homotopy classes \([M,S^n]\) where M is a closed and connected spin \((n+1)\)-manifold is called the n-th cohomotopy group \(\pi ^n(M)\) of M. Using homotopy theory it is known that \(\pi ^n(M) = H^n(M;{\mathbb {Z}}) \oplus {\mathbb {Z}}_2\). We will provide a geometrical description of the \({\mathbb {Z}}_2\) part in \(\pi ^n(M)\) analogous to Pontryagin’s computation of the
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Quasi-derivation relations for multiple zeta values revisited Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2020-11-25 Masanobu Kaneko, Hideki Murahara, Takuya Murakami
We take another look at the so-called quasi-derivation relations in the theory of multiple zeta values, by giving a certain formula for the quasi-derivation operator. In doing so, we are not only able to prove the quasi-derivation relations in a simpler manner but also give an analog of the quasi-derivation relations for finite multiple zeta values.
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Modular forms and q -analogues of modified double zeta values Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2020-11-11 Henrik Bachmann
We present explicit formulas for Hecke eigenforms as linear combinations of q-analogues of modified double zeta values. As an application, we obtain period polynomial relations and sum formulas for these modified double zeta values. These relations have similar shapes as the period polynomial relations of Gangl, Kaneko, and Zagier and the usual sum formulas for classical double zeta values.
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A note on the Sturm bound for Siegel modular forms of type ( k , 2) Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2020-10-30 Hirotaka Kodama
We study analogues of Sturm’s bounds for vector valued Siegel modular forms of type (k, 2), which was already studied by Sturm in the case of an elliptic modular form and by Choi–Choie–Kikuta, Poor–Yuen and Raum–Richter in the case of scalar valued Siegel modular forms.
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Twisted adjoint L -values, dihedral congruence primes and the Bloch–Kato conjecture Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2020-10-29 Neil Dummigan
We show that a dihedral congruence prime for a normalised Hecke eigenform f in \(S_k(\Gamma _0(D),\chi _D)\), where \(\chi _D\) is a real quadratic character, appears in the denominator of the Bloch–Kato conjectural formula for the value at 1 of the twisted adjoint L-function of f. We then use a formula of Zagier to prove that it appears in the denominator of a suitably normalised \(L(1,{\mathrm {ad}}^0(g)\otimes
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The contact geometry of the spatial circular restricted 3-body problem Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2020-09-10 WanKi Cho, Hyojin Jung, GeonWoo Kim
We show that a hypersurface of the regularized, spatial circular restricted three-body problem is of contact type whenever the energy level is below the first critical value (the energy level of the first Lagrange point) or if the energy level is slightly above it. A dynamical consequence is that there is no blue sky catastrophe in this energy range.
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On some classes of $${\mathbb {Z}}$$ Z -graded Lie algebras Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2020-07-09 Stefano Marini; Costantino Medori; Mauro Nacinovich
We study finite dimensional almost- and quasi-effective prolongations of nilpotent \({\mathbb {Z}}\)-graded Lie algebras, especially focusing on those having a decomposable reductive structural subalgebra. Our assumptions generalize effectiveness and algebraicity and are appropriate to obtain Levi–Malčev and Levi–Chevalley decompositions and precisions on the heigth and other properties of the prolongations
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A construction of p -adic Hurwitz–Lerch L -function Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2020-07-01 Selin Selen Özbek; Mehmet Cenkci
We derive the existence of p-adic Hurwitz–Lerch L-function by means of a method provided by Washington. This function is a generalization of the one-variable p-adic L-function of Kubota and Leopoldt, and two-variable p-adic L-function of Fox. We also deduce divisibility properties of generalized Apostol–Bernoulli polynomials, in particular establish Kummer-type congruences for them.
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A characterization of complex space forms via Laplace operators Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2020-06-25 Andrea Loi; Filippo Salis; Fabio Zuddas
Inspired by the work of Lu and Tian (Duke Math J 125(2):351–387, 2004), in this paper we address the problem of studying those Kähler manifolds satisfying the \(\Delta\)-property, i.e. such that on a neighborhood of each of its points the kth power of the Kähler Laplacian is a polynomial function of the complex Euclidean Laplacian, for all positive integer k (see below for its definition). We prove
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Differential geometry of immersed surfaces in three-dimensional normed spaces Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2020-06-18 Vitor Balestro; Horst Martini; Ralph Teixeira
In this paper we study curvature types of immersed surfaces in three-dimensional (normed or) Minkowski spaces. By endowing the surface with a normal vector field, which is a transversal vector field given by the ambient Birkhoff orthogonality, we get an analogue of the Gauss map. Then we can define concepts of principal, Gaussian, and mean curvatures in terms of the eigenvalues of the differential
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On the Chow ring of Fano varieties of type S 2 Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2020-06-09 Robert Laterveer
We show that certain Fano eightfolds (obtained as hyperplane sections of an orthogonal Grassmannian, and studied by Ito–Miura–Okawa–Ueda and by Fatighenti–Mongardi) have a multiplicative Chow–Künneth decomposition. As a corollary, the Chow ring of these eightfolds behaves like that of K3 surfaces.
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Linking complex analytic to nonstandard algebraic geometry Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2020-05-29 Adel Khalfallah; Siegmund Kosarew
In this paper, we sketch some constructions providing a link between complex-analytic geometry and nonstandard algebraic geometry via a categorical point of view. The analytic category is seen as a completed fiber of a family of nonstandard algebraic geometries by applying a standard part functor. We indicate how various notions of analytic objects fit into this context (as for example banachanalytic
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Explicit uniformizers for certain totally ramified extensions of the field of p -adic numbers Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2020-05-20 Hugues Bellemare; Antonio Lei
Let p be an odd prime number. We construct explicit uniformizers for the totally ramified extension \({\mathbb {Q}}_p(\zeta _{p^2},\root p \of {p})\) of the field of p-adic numbers \({\mathbb {Q}}_p\), where \(\zeta _{p^2}\) is a primitive \(p^2\)-th root of unity.
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On a type of maximal abelian torsion free subgroups of connected Lie groups Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2020-02-12 Abdelhak Abouqateb; Mehdi Nabil
For an arbitrary real connected Lie group G we define \(\mathrm {p}(G)\) as the maximal integer p such that \(\mathbb {Z}^p\) is isomorphic to a discrete subgroup of G and \(\mathrm {q}(G)\) is the maximal integer q such that \(\mathbb {R}^q\) is isomorphic to a closed subgroup of G. The aim of this paper is to investigate properties of these two invariants. We will show that if G is a noncompact connected
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Local Type II metrics with holonomy in $${\mathrm {G}}_2^*$$G2∗ Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2019-11-18 Christian Volkhausen
A list of possible holonomy groups with indecomposable holonomy representation contained in the exceptional, non-compact Lie group \({\mathrm {G}}_2^{*}\) was provided by Fino and Kath. The classification is due to the corresponding holonomy algebras and divided into Type I, II and III, depending on the dimension of the socle being 1, 2 or 3, respectively. It was also shown by Fino and Kath that all
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Completely replicable functions and symmetries Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2019-11-05 Bernhard Heim; Atsushi Murase
Completely replicable functions play an important role in number theory and finite group theory, in particular the Monstrous Moonshine. In this paper, we give a characterization of completely replicable functions by certain symmetries.
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The local invariant for scale structures on mapping spaces Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2019-11-04 Jungsoo Kang
A scale Hilbert space is a natural generalization of a Hilbert space which considers not only a single Hilbert space but a nested sequence of subspaces. Scale structures were introduced by H. Hofer, K. Wysocki, and E. Zehnder as a new concept of smooth structures in infinite dimensions. In this paper, we prove that scale structures on mapping spaces are completely determined by the dimension of domain
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Correction to: On Fourier coefficients of Siegel modular forms of degree two with respect to congruence subgroups Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2019-10-09 Masataka Chida, Hidenori Katsurada, Kohji Matsumoto
There are several inaccurate points and misprints in our article [1].
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Twisted component sums of vector-valued modular forms Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2019-10-09 Markus Schwagenscheidt; Brandon Williams
We construct isomorphisms between spaces of vector-valued modular forms for the dual Weil representation and certain spaces of scalar-valued modular forms in the case that the underlying finite quadratic module A has order p or 2p, where p is an odd prime. The isomorphisms are given by twisted sums of the components of vector-valued modular forms. Our results generalize work of Bruinier and Bundschuh
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Consequences of functional equations for pairs of p -adic L -functions Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2019-10-05 Cédric Dion; Florian Sprung
We prove consequences of functional equations of p-adic L-functions for elliptic curves at supersingular primes p. The results include a relationship between the leading and sub-leading terms (for which we use ideas of Wuthrich and Bianchi), a parity result of orders of vanishing, and invariance of Iwasaswa invariants under conjugate twists of the p-adic L-functions.
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Non-vanishing of Miyawaki type lifts Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2019-09-10 Henry H. Kim; Takuya Yamauchi
In this paper, we study the non-vanishing of the Miyawaki type lift in various situations. In the case of GSpin(2, 10) constructed in Kim and Yamauchi (Math Z 288(1–2):415–437, 2018), we use the fact that the Fourier coefficient at the identity is closely related to the Rankin–Selberg L-function of two elliptic cusp forms. In the case of the original Miyawaki lifts of Siegel cusp forms, we use the
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A ring of symmetric Hermitian modular forms of degree 2 with integral Fourier coefficients Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2019-09-03 Toshiyuki Kikuta
We determine the structure over \(\mathbb {Z}\) of a ring of symmetric Hermitian modular forms of degree 2 with integral Fourier coefficients whose weights are multiples of 4 when the base field is the Gaussian number field \(\mathbb {Q}(\sqrt{-1})\). Namely, we give a set of generators consisting of 24 modular forms. As an application of our structure theorem, we give the Sturm bounds for such Hermitian
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Analytic properties of twisted real-analytic Hermitian Klingen type Eisenstein series and applications Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2019-08-19 Soumya Das; Abhash Kumar Jha
We prove the meromorphic continuation and the functional equation of a twisted real-analytic Hermitain Eisenstein series of Klingen type, and as a consequence, deduce similar properties for the twisted Dirichlet series associated to a pair of Hermitian modular forms involving their Fourier–Jacobi coefficients. As an application of our result, we prove that infinitely many of the Fourier–Jacobi coefficients
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Willmore surfaces in spheres: the DPW approach via the conformal Gauss map Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2019-07-09 Josef F. Dorfmeister; Peng Wang
The paper builds a DPW approach of Willmore surfaces via conformal Gauss maps. As applications, we provide descriptions of minimal surfaces in \({\mathbb {R}}^{n+2}\), isotropic surfaces in \(S^4\) and homogeneous Willmore tori via the loop group method. A new example of a Willmore two-sphere in \(S^6\) without dual surfaces is also presented.
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Arithmetic of Catalan’s constant and its relatives Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2019-05-27 Wadim Zudilin
We prove that at least one of the six numbers \(\beta (2i)\) for \(i=1,\ldots ,6\) is irrational. Here \(\beta (s)=\sum _{k=0}^{\infty }(-1)^k(2k+1)^{-s}\) denotes Dirichlet’s beta function, so that \(\beta (2)\) is Catalan’s constant.
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One-line formula for automorphic differential operators on Siegel modular forms Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2019-04-27 Tomoyoshi Ibukiyama
We consider the Siegel upper half space \(H_{2m}\) of degree 2m and a subset \(H_m\times H_m\) of \(H_{2m}\) consisting of two \(m\times m\) diagonal block matrices. We consider two actions of \(Sp(m,{\mathbb R})\times Sp(m,{\mathbb R}) \subset Sp(2m,{\mathbb R})\), one is the action on holomorphic functions on \(H_{2m}\) defined by the automorphy factor of weight k on \(H_{2m}\) and the other is the
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The uniqueness of Weierstrass points with semigroup $$\langle a;b\rangle $$ ⟨ a ; b ⟩ and related semigroups Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2019-02-15 Marc Coppens
Assume a and \(b=na+r\) with \(n \ge 1\) and \(0\) then C is called a \(C_{a;b}\)-curve. In case \(r \ne a-1\) and \(b \ne a+1\) we prove C has no other point \(Q \ne P\) having Weierstrass semigroup equal to \(\), in which case we say that the Weierstrass semigroup \(\) occurs at most once. The curve \(C_{a;b}\) has genus \((a-1)(b-1)/2\) and the result is generalized to genus \(g<(a-1)(b-1)/2\).
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Functional equations of real analytic Jacobi Eisenstein series Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2019-01-14 Shin-ichiro Mizumoto
We prove the existence of meromorphic continuation and the functional equation of the real analytic Jacobi Eisenstein series of degree m and matrix index T in case T is a kernel form.
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On linear relations for L-values over real quadratic fields Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2018-11-22 Ren-He Su
In this paper, we give a method to construct a classical modular form from a Hilbert modular form. By applying this method, we can get linear formulas which relate the Fourier coefficients of the Hilbert and classical modular forms. The paper focuses on the Hilbert modular forms over real quadratic fields. We will state a construction of relations between the special values of L-functions, especially
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A motivic study of generalized Burniat surfaces Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2018-11-01 Chris Peters
Generalized Burniat surfaces are surfaces of general type with \(p_g=q\) and Euler number \(e=6\) obtained by a variant of Inoue’s construction method for the classical Burniat surfaces. I prove a variant of the Bloch conjecture for these surfaces. The method applies also to the so-called Sicilian surfaces introduced by Bauer et al. in (J Math Sci Univ Tokyo 22(2–15):55–111, 2015. arXiv:1409.1285v2)
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Modular forms for the $$A_{1}$$ A 1 -tower Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2018-10-10 Martin Woitalla
In the 1960s Igusa determined the graded ring of Siegel modular forms of genus two. He used theta series to construct \(\chi _{5}\), the cusp form of lowest weight for the group \({\text {Sp}}(2,\mathbb {Z})\). In 2010 Gritsenko found three towers of orthogonal type modular forms which are connected with certain series of root lattices. In this setting Siegel modular forms can be identified with the
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A duality theorem for Tate–Shafarevich groups of curves over algebraically closed fields Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2018-10-04 Timo Keller
In this note, we prove a duality theorem for the Tate–Shafarevich group of a finite discrete Galois module over the function field K of a curve over an algebraically closed field: there is a perfect duality of finite groups for F a finite étale Galois module on K of order invertible in K and with \(F' = {{\mathrm{Hom}}}(F,\mathbf{Q}/\mathbf {Z}(1))\). Furthermore, we prove that \(\mathrm {H}^1(K,G)
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Semisimple weakly symmetric pseudo-Riemannian manifolds Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2018-08-29 Zhiqi Chen; Joseph A. Wolf
We develop the classification of weakly symmetric pseudo-Riemannian manifolds G / H where G is a semisimple Lie group and H is a reductive subgroup. We derive the classification from the cases where G is compact, and then we discuss the (isotropy) representation of H on the tangent space of G / H and the signature of the invariant pseudo-Riemannian metric. As a consequence we obtain the classification
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Non-vanishing of products of Fourier coefficients of modular forms of half-integral weight Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2018-05-16 Winfried Kohnen
We prove a non-vanishing result in weight aspect for the product of two Fourier coefficients of a Hecke eigenform of half-integral weight.
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Forms and currents defining generalized p -Kähler structures Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2018-03-29 Lucia Alessandrini
This paper is devoted, first of all, to give a complete unified proof of the characterization theorem for compact generalized Kähler manifolds. The proof is based on the classical duality between “closed” positive forms and “exact” positive currents. In the last part of the paper we approach the general case of non compact complex manifolds, where “exact” positive forms seem to play a more significant
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Correction to: Split buildings of type \(\mathsf {F_4}\) in buildings of type \(\mathsf {E_6}\) Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2018-02-09 Anneleen De Schepper,N. S. Narasimha Sastry,Hendrik Van Maldeghem
The original version of this article unfortunately contained a mistake in the author’s name N. S. Narasimha Sastry. The corrected name is given above.
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Asymptotic analysis of expectations of plane partition statistics Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2018-02-06 Ljuben Mutafchiev
Assuming that a plane partition of the positive integer n is chosen uniformly at random from the set of all such partitions, we propose a general asymptotic scheme for the computation of expectations of various plane partition statistics as n becomes large. The generating functions that arise in this study are of the form Q(x)F(x), where \(Q(x)=\prod _{j=1}^\infty (1-x^j)^{-j}\) is the generating function
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Split buildings of type $$\mathsf {F_4}$$ F 4 in buildings of type $$\mathsf {E_6}$$ E 6 Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2018-01-16 Anneleen De Schepper; N. S. Narasimha Sastry; Hendrik Van Maldeghem
A symplectic polarity of a building \(\varDelta \) of type \(\mathsf {E_6}\) is a polarity whose fixed point structure is a building of type \(\mathsf {F_4}\) containing residues isomorphic to symplectic polar spaces (i.e., so-called split buildings of type \(\mathsf {F_4}\)). In this paper, we show in a geometric way that every building of type \(\mathsf {E_6}\) contains, up to conjugacy, a unique
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Why there is no an existence theorem for a convex polytope with prescribed directions and perimeters of the faces? Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2017-12-11 Victor Alexandrov
We choose some special unit vectors \({\mathbf {n}}_1,\ldots ,{\mathbf {n}}_5\) in \({\mathbb {R}}^3\) and denote by \({\mathscr {L}}\subset {\mathbb {R}}^5\) the set of all points \((L_1,\ldots ,L_5)\in {\mathbb {R}}^5\) with the following property: there exists a compact convex polytope \(P\subset {\mathbb {R}}^3\) such that the vectors \({\mathbf {n}}_1,\ldots ,{\mathbf {n}}_5\) (and no other vector)
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Seifert fibrations of lens spaces Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2017-10-23 Hansjörg Geiges; Christian Lange
We classify the Seifert fibrations of any given lens space L(p, q). Starting from any pair of coprime non-zero integers \(\alpha _1^0,\alpha _2^0\), we give an algorithmic construction of a Seifert fibration \(L(p,q)\rightarrow S^2(\alpha |\alpha _1^0|,\alpha |\alpha _2^0|)\), where the natural number \(\alpha \) is determined by the algorithm. This algorithm produces all possible Seifert fibrations
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On Ikehara type Tauberian theorems with $$O(x^\gamma )$$ O ( x γ ) remainders Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2017-09-12 Michael Müger
Motivated by analytic number theory, we explore remainder versions of Ikehara’s Tauberian theorem yielding power law remainder terms. More precisely, for \(f:[1,\infty )\rightarrow {\mathbb R}\) non-negative and non-decreasing we prove \(f(x)-x=O(x^\gamma )\) with \(\gamma <1\) under certain assumptions on f. We state a conjecture concerning the weakest natural assumptions and show that we cannot hope
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Triviality of Iwasawa module associated to some abelian fields of prime conductors Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2017-09-11 Humio Ichimura
Let p be an odd prime number and \(\ell \) an odd prime number dividing \(p-1\). We denote by \(F=F_{p,\ell }\) the real abelian field of conductor p and degree \(\ell \), and by \(h_F\) the class number of F. For a prime number \(r \ne p,\,\ell \), let \(F_{\infty }\) be the cyclotomic \(\mathbb {Z}_r\)-extension over F, and \(M_{\infty }/F_{\infty }\) the maximal pro-r abelian extension unramified
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Isospectral nearly Kähler manifolds Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2017-08-22 J. J. Vásquez
We give a systematic way to construct almost conjugate pairs of finite subgroups of \(\mathrm {Spin}(2n+1)\) and \({{\mathrm{Pin}}}(n)\) for \(n\in {\mathbb {N}}\) sufficiently large. As a geometric application, we give an infinite family of pairs \(M_1^{d_n}\) and \(M_2^{d_n}\) of nearly Kähler manifolds that are isospectral for the Dirac and Laplace operator with increasing dimensions \(d_n>6\).
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Theta functions on tube domains Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2017-06-28 Josef F. Dorfmeister; Sebastian Walcher
We discuss generalizations of classical theta series, requiring only some basic properties of the classical setting. As it turns out, the existence of a generalized theta transformation formula implies that the series is defined over a quasi-symmetric Siegel domain. In particular the exceptional symmetric tube domain does not admit a theta function.
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Motives of derived equivalent K3 surfaces Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2017-06-07 D. Huybrechts
We observe that derived equivalent K3 surfaces have isomorphic Chow motives. The result holds more generally for arbitrary surfaces, as pointed out by Charles Vial.
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A brief note on the coarea formula Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2017-06-03 Lucio Cadeddu; Maria Antonietta Farina
In this note we consider a special case of the famous Coarea Formula whose initial proof (for functions from any Riemannian manifold of dimension 2 into \({\mathbb {R}}\)) is due to Kronrod (Uspechi Matem Nauk 5(1):24–134, 1950) and whose general proof (for Lipschitz maps between two Riemannian manifolds of dimensions n and p) is due to Federer (Am Math Soc 93:418–491, 1959). See also Maly et al. (Trans
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Topological invariants from quantum group $$\mathcal {U}_{\xi }\mathfrak {sl}(2|1)$$ U ξ sl ( 2 | 1 ) at roots of unity Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2017-05-24 Ngoc Phu Ha
In this article we construct link invariants and 3-manifold invariants from the quantum group associated with the Lie superalgebra \(\mathfrak {sl}(2|1)\). The construction is based on nilpotent irreducible finite dimensional representations of quantum group \(\mathcal {U}_{\xi }\mathfrak {sl}(2|1)\) where \(\xi \) is a root of unity of odd order. These constructions use the notion of modified trace
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The Bott–Samelson theorem for positive Legendrian isotopies Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2017-05-18 Lucas Dahinden
The classical Bott–Samelson theorem states that if on a Riemannian manifold all geodesics issuing from a certain point return to this point, then the universal cover of the manifold has the cohomology ring of a compact rank one symmetric space. This result on geodesic flows has been generalized to Reeb flows and partially to positive Legendrian isotopies by Frauenfelder–Labrousse–Schlenk. We prove
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Period of the adelic Ikeda lift for U ( m , m ) Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2017-04-17 Hidenori Katsurada
We give a period formula for the adelic Ikeda lift of an elliptic modular form f for U(m, m) in terms of special values of the adjoint L-functions of f. This is an adelic version of Ikeda’s conjecture on the period of the classical Ikeda lift for U(m, m).
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A remark on the structure of torsors under an affine group scheme Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2017-04-13 Christopher Deninger
It is well known that all torsors under an affine algebraic group over an algebraically closed field are trivial. We note that under suitable conditions this also holds if the group is not necessarily of finite type. This has an application to isomorphisms of fibre functors on neutral Tannakian categories.
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Maass Spezialschar of level N Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2017-02-22 Bernhard Heim
In this paper the image of the Saito–Kurokawa lift of level N with Dirichlet character is studied. We give a new characterization of this so called Maass Spezialschar of level N by symmetries involving Hecke operators related to \(\Gamma _0(N)\). We finally obtain for all prime numbers p local Maass relations. This generalizes known results for level \(N=1\).
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Critical vertices in k-connected digraphs Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2017-02-06 W. Mader
It is proved that every non-complete, finite digraph of connectivity number k has a fragment F containing at most k critical vertices. The following result is a direct consequence: every k-connected, finite digraph D of minimum out- and indegree at least \(2k+ m- 1\) for positive integers k, m has a subdigraph H of minimum outdegree or minimum indegree at least \(m-1\) such that \(D - x\) is k-connected
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Ends and tangles Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2017-01-18 Reinhard Diestel
We show that an arbitrary infinite graph can be compactified by its \({\aleph _0}\)-tangles in much the same way as the ends of a locally finite graph compactify it in its Freudenthal compactification. In general, the ends then appear as a subset of its \({\aleph _0}\)-tangles. The \({\aleph _0}\)-tangles of a graph are shown to form an inverse limit of the ultrafilters on the sets of components obtained
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On a problem of Erdős and Moser Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2017-01-09 Béla Bollobás; Alex Scott
A set A of vertices in an r-uniform hypergraph \(\mathcal H\) is covered in \(\mathcal H\) if there is some vertex \(u\not \in A\) such that every edge of the form \(\{u\}\cup B\), \(B\in A^{(r-1)}\) is in \(\mathcal H\). Erdős and Moser (J Aust Math Soc 11:42–47, 1970) determined the minimum number of edges in a graph on n vertices such that every k-set is covered. We extend this result to r-uniform
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Degree sequences and edge connectivity Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2017-01-05 Matthias Kriesell
For each positive integer k, we give a finite list C(k) of Bondy–Chvátal type conditions on a nondecreasing sequence \(d=(d_1,\dots ,d_n)\) of nonnegative integers such that every graph on n vertices with degree sequence at least d is k-edge-connected. These conditions are best possible in the sense that whenever one of them fails for d then there is a graph on n vertices with degree sequence at least
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Trees and circle orders Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2017-01-05 William T. Trotter
This paper continues a recent resurgence of interest in combinatorial properties of a poset that are associated with graph properties of its cover graph and order diagram. The following two theorems appearing in a 1977 paper of Trotter and Moore have played important roles in motivating this more modern research: (1) The dimension of a poset is at most 3 when its cover graph is at tree; (2) The dimension
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On the existence of real R-matrices for virtual link invariants Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2017-01-04 Guus Regts; Alexander Schrijver; Bart Sevenster
We characterize the virtual link invariants that can be described as partition function of a real-valued R-matrix, by being weakly reflection positive. Weak reflection positivity is defined in terms of joining virtual link diagrams, which is a specialization of joining virtual link diagram tangles. Basic techniques are the first fundamental theorem of invariant theory, the Hanlon–Wales theorem on the
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Spanning quadrangulations of triangulated surfaces Abh. Math. Semin. Univ. Hambg. (IF 0.471) Pub Date : 2017-01-04 André Kündgen; Carsten Thomassen
In this paper we study alternating cycles in graphs embedded in a surface. We observe that 4-vertex-colorability of a triangulation on a surface can be expressed in terms of spanninq quadrangulations, and we establish connections between spanning quadrangulations and cycles in the dual graph which are noncontractible and alternating with respect to a perfect matching. We show that the dual graph of