• Math. Z. (IF 0.881) Pub Date : 2020-08-25
Victor W. Guillemin, Eva Miranda, Jonathan Weitsman

We study the formal geometric quantization of $$b^m$$-symplectic manifolds equipped with Hamiltonian actions of a torus T with nonzero leading modular weight. The resulting virtual $$T-$$modules are finite dimensional when m is odd, as in [4]; when m is even, these virtual modules are not finite dimensional, and we compute the asymptotics of the representations for large weight.

更新日期：2020-08-25
• Math. Z. (IF 0.881) Pub Date : 2020-08-20
Eduard Looijenga

Kreck and Yang Su recently gave counterexamples to a version of the Torelli theorem for hyperkählerian manifolds as stated by Verbitsky. We extract the correct statement and give a short proof of it. We also revisit a few of its consequences, some of which are given new (shorter) proofs, and ask some questions.

更新日期：2020-08-20
• Math. Z. (IF 0.881) Pub Date : 2020-08-17
Peter Buser, Eran Makover, Bjoern Muetzel, Robert Silhol

We study the energy distribution of harmonic 1-forms on a compact hyperbolic Riemann surface S where a short closed geodesic is pinched. If the geodesic separates the surface into two parts, then the Jacobian variety of S develops into a variety that splits. If the geodesic is nonseparating then the Jacobian degenerates. The aim of this work is to get insight into this process and give estimates in

更新日期：2020-08-18
• Math. Z. (IF 0.881) Pub Date : 2020-08-17
Yan Li, Xiaohua Zhu

In this paper, we compute Tian’s $$\alpha _{m,k}^{K\times K}$$-invariant on a polarized G-group compactification, where K denotes a maximal compact subgroup of a connected complex reductive group G. We prove that Tian’s conjecture (see Conjecture 1.1 below) is true for $$\alpha _{m,k}^{K\times K}$$-invariant on such manifolds when $$k=1$$, but it fails in general by producing counter-examples when

更新日期：2020-08-17
• Math. Z. (IF 0.881) Pub Date : 2020-08-12
Yuichiro Hoshi, Takahiro Murotani, Shota Tsujimura

In the present paper, we establish a “group-theoretic” algorithm for reconstructing, from the étale fundamental group of a suitable proper normal variety over a real closed field, the geometric subgroup of the étale fundamental group of the proper normal variety.

更新日期：2020-08-12
• Math. Z. (IF 0.881) Pub Date : 2020-08-12
Changjian Fu, Shengfei Geng, Pin Liu

We study cluster algebras arising from cluster tubes. We obtain categorical interpretations for g-vectors, c-vectors and denominator vectors for cluster algebras of type $$\mathrm {C}$$ with respect to arbitrary initial seeds. In particular, a denominator theorem has been proved, which enables us to establish the linearly independence of denominator vectors of cluster variables from the same cluster

更新日期：2020-08-12
• Math. Z. (IF 0.881) Pub Date : 2020-08-11
Bao-Wei Wang, Guo-Hua Zhang

Diophantine approximation in dynamical systems concerns the Diophantine properties of the orbits. In classic Diophantine approximation, the powerful mass transference principle established by Beresnevich and Velani provides a general principle to the dimension for a limsup set. In this paper, we aim at finding a general principle for the dimension of the limsup set arising in a general expanding dynamical

更新日期：2020-08-11
• Math. Z. (IF 0.881) Pub Date : 2020-08-11
Changjian Su

A formula for the structure constants of the multiplication of Schubert classes is obtained in (Rebecca and Allen. arXiv preprint arXiv:1909.05283, 2019). In this note, we prove analogous formulae for the Chern–Schwartz–MacPherson (CSM) classes and Segre–Schwartz–MacPherson (SSM) classes of Schubert cells in the flag variety. By the equivalence between the CSM classes and the stable basis elements

更新日期：2020-08-11
• Math. Z. (IF 0.881) Pub Date : 2020-08-10
David Barnes, J. P. C. Greenlees, Magdalena Kędziorek

Equipping a non-equivariant topological $$\text {E}_\infty$$-operad with the trivial G-action gives an operad in G-spaces. For a G-spectrum, being an algebra over this operad does not provide any multiplicative norm maps on homotopy groups. Algebras over this operad are called naïve-commutative ring G-spectra. In this paper we take $$G=SO(2)$$ and we show that commutative algebras in the algebraic

更新日期：2020-08-10
• Math. Z. (IF 0.881) Pub Date : 2020-08-09
Tom Bachmann

Let k be a field and denote by $$\mathcal {SH}(k)$$ the motivic stable homotopy category. Recall its full subcategory $$\mathcal {SH}(k)^{{\text {eff}}\heartsuit }$$ (Bachmann in J Topol 10(4):1124–1144. arXiv:1610.01346, 2017). Write $$\mathrm {NAlg}(\mathcal {SH}(k))$$ for the category of $${\mathrm {S}\mathrm {m}}$$-normed spectra (Bachmann-Hoyois in arXiv:1711.03061, 2017); recall that there is

更新日期：2020-08-10
• Math. Z. (IF 0.881) Pub Date : 2020-08-09
Werner Müller, Frédéric Rochon

For $$d=2n+1$$ a positive odd integer, we consider sequences of arithmetic subgroups of $${\text {SO}}_0(d,1)$$ and yielding corresponding hyperbolic manifolds of finite volume and show that, under appropriate and natural assumptions, the torsion of the associated cohomology groups grows exponentially.

更新日期：2020-08-10
• Math. Z. (IF 0.881) Pub Date : 2020-08-09
Shen-Ning Tung

Using p-adic local Langlands correspondence for $${\text {GL}}_2(\mathbb {Q}_2)$$ and an ordinary $$R = \mathbb {T}$$ theorem, we prove that the support of patched modules for quaternionic forms meet every irreducible component of the potentially semi-stable deformation ring. This gives a new proof of the Breuil–Mézard conjecture for 2-dimensional representations of the absolute Galois group of $$\mathbb 更新日期：2020-08-10 • Math. Z. (IF 0.881) Pub Date : 2020-08-08 Thomas Mettler We show that the metrisability of an oriented projective surface is equivalent to the existence of pseudo-holomorphic curves. A projective structure \({\mathfrak {p}}$$ and a volume form $$\sigma$$ on an oriented surface M equip the total space of a certain disk bundle $$Z\rightarrow M$$ with a pair $$(J_{{\mathfrak {p}}},{\mathfrak {J}}_{{\mathfrak {p}},\sigma })$$ of almost complex structures. A

更新日期：2020-08-09
• Math. Z. (IF 0.881) Pub Date : 2020-08-08
Nicolas Bédaride, Arnaud Hilion, Martin Lustig

We explain and restate the results from our recent paper [2] in standard language for substitutions and S-adic systems in symbolic dynamics. We then produce as rather direct application an S-adic system (with finite set of substitutions S on d letters) that is minimal and has d distinct ergodic probability measures. As second application we exhibit a formula that allows an efficient practical computation

更新日期：2020-08-09
• Math. Z. (IF 0.881) Pub Date : 2020-08-08
Henrik Kreidler, Sita Siewert

The representation theorems of Gelfand and Kakutani for commutative C*-algebras and AM- and AL-spaces are the basis for the Koopman linearization of topological and measure-preserving dynamical systems. In this article we prove versions of these results for dynamics on topological and measurable Banach bundles and the corresponding weighted Koopman representations on Banach modules.

更新日期：2020-08-08
• Math. Z. (IF 0.881) Pub Date : 2020-08-07
Filippo Ambrosio

We define the group analogue of birational sheets, a construction performed by Losev for reductive Lie algebras. For G semisimple simply connected, we describe birational sheets in terms of Lusztig–Spaltenstein induction and we prove that they form a partition of G, and that they are unibranch varieties with smooth normalization by means of a local study.

更新日期：2020-08-08
• Math. Z. (IF 0.881) Pub Date : 2020-08-07
Elizabeth Gasparim, Luiz A. B. San Martin, Fabricio Valencia

We describe isotropic orbits for the restricted action of a subgroup of a Lie group acting on a symplectic manifold by Hamiltonian symplectomorphisms and admitting an Ad*-equivariant moment map. We obtain examples of Lagrangian orbits of complex flag manifolds, of cotangent bundles of orthogonal Lie groups, and of products of flags. We introduce the notion of infinitesimally tight and study the intersection

更新日期：2020-08-08
• Math. Z. (IF 0.881) Pub Date : 2020-08-07
Anna Fino, Nicoletta Tardini

We study Hermitian metrics whose Bismut connection $$\nabla ^B$$ satisfies the first Bianchi identity in relation to the SKT condition and the parallelism of the torsion of the Bimut connection. We obtain a characterization of complex surfaces admitting Hermitian metrics whose Bismut connection satisfy the first Bianchi identity and the condition $$R^B(x,y,z,w)=R^B(Jx,Jy,z,w)$$, for every tangent vectors

更新日期：2020-08-08
• Math. Z. (IF 0.881) Pub Date : 2020-08-06
Sumit Chandra Mishra

Let K be a complete discretely valued field with the residue field $$\kappa$$. Let F be the function field of a smooth, projective, geometrically integral curve over K and $$\mathscr {X}$$ be a regular proper model of F such that the reduced special fibre X is a union of regular curves with normal crossings. Suppose that the graph associated to $$\mathscr {X}$$ is a tree (e.g. $$F = K(t)$$). Let L/F

更新日期：2020-08-06
• Math. Z. (IF 0.881) Pub Date : 2020-08-04
Ken Sumi

We show that the space of theta functions on tropical tori is identified with a convex polyhedron. We also show a Riemann-Roch inequality for tropical abelian surfaces by calculating the self-intersection numbers of divisors.

更新日期：2020-08-04
• Math. Z. (IF 0.881) Pub Date : 2020-07-15
Ananth N. Shankar, Rong Zhou

We study the formal neighbourhood of a point in the $$\mu$$-ordinary locus of an integral model of a Hodge type Shimura variety. We show that this formal neighbourhood has a structure of a “shifted cascade”. Moreover we show that the CM points on the formal neighbourhood are dense and that the identity section of the shifted cascade corresponds to a lift of the abelian variety which has a characterization

更新日期：2020-07-15
• Math. Z. (IF 0.881) Pub Date : 2020-07-15
Liuyang Zhang

In this paper, we study Lagrangian surfaces satisfying $$\nabla ^*T=0$$ , where $$T=-2\nabla ^*(\check{A}\lrcorner \omega )$$ and $$\check{A}$$ is the Lagrangian trace-free second fundamental form. We obtain a gap lemma for such a Lagrangian surface.

更新日期：2020-07-15
• Math. Z. (IF 0.881) Pub Date : 2020-07-13
Shiquan Ruan, Xintian Wang

The present paper focuses on the study of t-stabilities on a triangulated category in the sense of Gorodentsev, Kuleshov and Rudakov. We give an equivalent description for the finest t-stabilities on certain triangulated category and, describe the semistable subcategories and last HN-triangles for coherent sheaves in $$D^b(\mathrm{coh\,}{{\mathbb {X}}})$$, which is the bounded derived category of coherent

更新日期：2020-07-13
• Math. Z. (IF 0.881) Pub Date : 2020-07-12
Ljudevit Palle

In their work Ikromov and Müller (Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra. Princeton University Press, Princeton, 2016) proved the full range $$L^p-L^2$$ Fourier restriction estimates for a very general class of hypersurfaces in $${\mathbb {R}}^3$$ which includes the class of real analytic hypersurfaces. In this article we partly extend their results to the mixed

更新日期：2020-07-13
• Math. Z. (IF 0.881) Pub Date : 2020-07-11
Caiyan Li

In this paper, we derive that every n-dimensional ($$2\le n\le 7$$) special Lagrangian cones in $${\mathbb {R}}^{n}\times {\mathbb {R}}^{n}$$ with flat normal bundle must be flat. And we also derive a rigidity result under a certain restriction on Gauss map.

更新日期：2020-07-13
• Math. Z. (IF 0.881) Pub Date : 2020-07-09
Jan Hendrik Bruinier, Markus Schwagenscheidt

We evaluate regularized theta lifts for Lorentzian lattices in three different ways. In particular, we obtain formulas for their values at special points involving coefficients of mock theta functions. By comparing the different evaluations, we derive recurrences for the coefficients of mock theta functions, such as Hurwitz class numbers, Andrews’ spt-function, and Ramanujan’s mock theta functions

更新日期：2020-07-09
• Math. Z. (IF 0.881) Pub Date : 2020-07-08
Petar Bakić, Marcela Hanzer

In this paper we give the description of generic representations of metaplectic groups over p-adic fields in terms of their Langlands parameters and calculate their theta lifts on all levels for any tower of odd orthogonal groups. We also describe precisely all the occurrences of the failure of the standard module conjecture for metaplectic groups.

更新日期：2020-07-08
• Math. Z. (IF 0.881) Pub Date : 2020-07-08
An-Min Li, Li Sheng

Let f be a smooth plurisubharmonic function which solves \begin{aligned} \det (f_{i\bar{\jmath }})=1\;\;\;\;\;\;\text{ on } \;\;\;\mathbb C^n. \end{aligned} Suppose that the metric $$\omega _{f}=\sqrt{-1}f_{i\bar{\jmath }}dz_{i}\wedge d\bar{z}_{j}$$ is complete and f satisfies the growth condition \begin{aligned} \mathsf N_{0}^{-1}(1+|z|^2)\le f\le \mathsf N_{0}(1+ |z|^2),\;\;\;\; \text{ as }\;\;\; 更新日期：2020-07-08 • Math. Z. (IF 0.881) Pub Date : 2020-07-04 Mohamed Saïdi Let X be a proper, smooth, and geometrically connected curve of genus $$g(X)\ge 1$$ over a p-adic local field. We prove that there exists an effectively computable open affine subscheme $$U\subset X$$ with the property that $${\text {period}}(X)=1$$, and $${\text {index}}(X)$$ equals 1 or 2 (resp. $${\text {period}}(X)={\text {index}}(X)=1$$, assuming $${\text {period}}(X)={\text {index}}(X)$$), if 更新日期：2020-07-05 • Math. Z. (IF 0.881) Pub Date : 2020-07-04 Nicolas Addington, Andrew Wray Bridgeland and Maciocia showed that a complex Enriques surface X has no Fourier–Mukai partners apart from itself: that is, if $$D^b(X) \cong D^b(Y)$$ then $$X \cong Y$$. We extend this to twisted Fourier–Mukai partners: if $$\alpha$$ is the non-trivial element of $${{\,\mathrm{Br}\,}}(X) = {\mathbb {Z}}/2$$ and $$D^b(X,\alpha ) \cong D^b(Y,\beta )$$, then $$X \cong Y$$ and $$\beta$$ is non-trivial 更新日期：2020-07-05 • Math. Z. (IF 0.881) Pub Date : 2020-07-03 Dor Mezer Let $${\mathbb {F}}$$ be a non-archimedean local field of characteristic different from 2. We consider distributions on $$\mathrm {GL}(n+1,{\mathbb {F}})$$ which are invariant under the adjoint action of $$\mathrm {GL}(n,{\mathbb {F}})$$. We prove that any such distribution is invariant under transposition. This implies that the restriction to $$\mathrm {GL}(n,{{\mathbb {F}}})$$ of any irreducible 更新日期：2020-07-03 • Math. Z. (IF 0.881) Pub Date : 2020-07-03 Chuanfang Ge, Jiansheng Geng, Zhaowei Lou In the present paper, we prove an infinite dimensional reversible Kolmogorov-Arnold-Moser (KAM) theorem. As an application, we study the existence of KAM tori for a class of two dimensional (2D) non-Hamiltonian completely resonant beam equations with derivative nonlinearities. The Birkhoff normal form theory is also used since there are no external parameters in the equations. 更新日期：2020-07-03 • Math. Z. (IF 0.881) Pub Date : 2020-07-03 Jinshou Gao, Zhangjian Hu Suppose D is a bounded strongly pseudoconvex domain in $${{\mathbb {C}}}^n$$ with smooth boundary, and let $$\rho$$ be its defining function. For $$1< p<\infty$$ and $$\alpha >-1$$, we show that the weighted Bergman projection $$P_\alpha$$ is bounded on $$L^p(D, |\rho |^\alpha dV)$$. With non-isotropic estimates for $$\overline{\partial }$$ and Stein’s theorem on non-tangential maximal operators 更新日期：2020-07-03 • Math. Z. (IF 0.881) Pub Date : 2020-07-03 Tak Wing Ching, Kai Man Tsang It is widely conjectured that every sufficiently large integer satisfying certain necessary congruence conditions is the sum of 4 cubes of prime numbers. As an approximation to this conjecture, we shall establish two results in this paper. Firstly, we show that every large odd integer is the sum of a prime, 4 cubes of primes and 15 powers of 2. Secondly, we show that the conjecture is true for at least 更新日期：2020-07-03 • Math. Z. (IF 0.881) Pub Date : 2020-07-02 Qun Chen, Linlin Sun In this note, we prove conformal lower bounds for Dirac operators of submanifolds in terms of conformal and extrinsic quantities. 更新日期：2020-07-02 • Math. Z. (IF 0.881) Pub Date : 2020-07-02 Alexander Perry Given a finite group action on a (suitably enhanced) triangulated category linear over a field, we establish a formula for the Hochschild cohomology of the category of invariants, assuming the order of the group is coprime to the characteristic of the base field. The formula shows that the cohomology splits canonically with one summand given by the invariant subspace of the Hochschild cohomology of 更新日期：2020-07-02 • Math. Z. (IF 0.881) Pub Date : 2020-07-02 Enrique Chávez-Martínez, Daniel Duarte, Arturo Giles Flores We introduce a higher-order version of the tangent map of a morphism and find a matrix representation. We then apply this matrix to solve a conjecture by Yasuda regarding the semigroup of the higher Nash blowup of formal curves. We first show that the conjecture is true for toric curves. We conclude by exhibiting a family of non-monomial curves where the conjecture fails. 更新日期：2020-07-02 • Math. Z. (IF 0.881) Pub Date : 2020-07-01 Christopher Daw, Alexander Gorodnik, Emmanuel Ullmo We conjecture that the set of homogeneous probability measures on the maximal Satake compactification of an arithmetic locally symmetric space $$S=\Gamma \backslash G/K$$ is compact. More precisely, given a sequence of homogeneous probability measures on S, we expect that any weak limit is homogeneous with support contained in precisely one of the boundary components (including S itself). We introduce 更新日期：2020-07-01 • Math. Z. (IF 0.881) Pub Date : 2020-07-01 Godofredo Iommi, Anibal Velozo We study suspension flows defined over sub-shifts of finite type with continuous roof functions. We prove the existence of suspension flows with uncountably many ergodic measures of maximal entropy. More generally, we prove that any suspension flow defined over a sub-shift of finite type can be perturbed (by an arbitrarily small perturbation) so that the resulting flow has uncountably many ergodic 更新日期：2020-07-01 • Math. Z. (IF 0.881) Pub Date : 2020-07-01 Doowon Koh, Thang Pham, Chun-Yen Shen, Le Anh Vinh We study a variant of the Erdős–Falconer distance problem in the setting of finite fields. More precisely, let E and F be sets in $$\mathbb {F}_q^d$$, and $$\Delta (E), \Delta (F)$$ be corresponding distance sets. We prove that if $$|E||F|\ge Cq^{d+\frac{1}{3}}$$ for a sufficiently large constant C, then the set $$\Delta (E)+\Delta (F)$$ covers at least a half of all distances. Our result in odd dimensional 更新日期：2020-07-01 • Math. Z. (IF 0.881) Pub Date : 2020-07-01 Paul Sobaje Let G be a simple algebraic group over an algebraically closed field of prime characteristic. If M is a finite dimensional G-module that is projective over the Frobenius kernel of G, then its character is divisible by the character of the Steinberg module. In this paper we study such quotients, showing that if M is an indecomposable tilting module, then the multiplicities of the orbit sums appearing 更新日期：2020-07-01 • Math. Z. (IF 0.881) Pub Date : 2020-07-01 Tong Zhou, Wen-Xin Qin By introducing for monotone recurrence relations pseudo solutions, which are analogues of pseudo orbits of dynamical systems, we show that for general monotone recurrence relations the rotation set is closed, and each element in the rotation set is realized by a Birkhoff orbit. Moreover, if there is an orbit without rotation number, then the system has positive topological entropy, and we can construct 更新日期：2020-07-01 • Math. Z. (IF 0.881) Pub Date : 2020-06-30 Bo-Yong Chen, Xu Wang Based on Harnack’s inequality and convex analysis we show that each plurisubharmonic function is locally BUO (bounded upper oscillation) with respect to polydiscs of finite type but not for arbitrary polydiscs. We also show that each function in the Lelong class is globally BUO with respect to all polydiscs. A dimension-free BUO estimate is obtained for the logarithm of the modulus of a complex polynomial 更新日期：2020-06-30 • Math. Z. (IF 0.881) Pub Date : 2020-06-30 Andrea Tamburelli In this paper we combine our recent work on regular globally hyperbolic maximal anti-de Sitter structures with the classical theory of globally hyperbolic maximal Cauchy-compact anti-de Sitter manifolds in order to define an augmented moduli space. Moreover, we introduce a coordinate system in this space that resembles the complex Fenchel–Nielsen coordinates for hyperbolic quasi-Fuchsian manifolds 更新日期：2020-06-30 • Math. Z. (IF 0.881) Pub Date : 2020-06-24 Anders Björn, Jana Björn, Nageswari Shanmugalingam We show that, under certain geometric conditions, there are no nonconstant quasiminimizers with finite pth power energy in a (not necessarily complete) metric measure space equipped with a globally doubling measure supporting a global $$p$$-Poincaré inequality. The geometric conditions are that either (a) the measure has a sufficiently strong volume growth at infinity, or (b) the metric space is annularly 更新日期：2020-06-25 • Math. Z. (IF 0.881) Pub Date : 2020-06-19 Francesca Aicardi, Jesús Juyumaya In the original publication, there are missing symbols in Theorem 1 and two missing lines in Theorem 3 (cf. https://arxiv.org/pdf/1607.04841v5.pdf). 更新日期：2020-06-22 • Math. Z. (IF 0.881) Pub Date : 2020-06-16 Yuxiang Li, Zhipeng Zhou Let (M, g) be a smooth compact Riemiannian manifold without boundary and $$g_k$$ be a metric conformal to g. Suppose $$\text{ vol }(M,g_k)+\Vert R_k\Vert _{L^p(M,g_k)}\frac{n}{2}$$. We will use the 3-circles theorem to study the bubble tree convergence of $$g_k$$. 更新日期：2020-06-16 • Math. Z. (IF 0.881) Pub Date : 2020-06-16 Yuanqing Cai We describe the twisted doubling integrals of Cai–Friedberg–Ginzburg–Kaplan in a conceptual way. This also extends the construction to the quaternionic unitary groups. We carry out the unfolding argument uniformly in this article. To do so, we define a family of degenerate Whittaker coefficients that are suitable in this setup and study some of their properties. We also prove certain related global 更新日期：2020-06-16 • Math. Z. (IF 0.881) Pub Date : 2020-06-15 Bin Xu Arthur classified the discrete automorphic representations of symplectic and orthogonal groups over a number field by that of the general linear groups. In this classification, those that are not from endoscopic lifting correspond to pairs $$(\phi , b)$$, where $$\phi$$ is an irreducible unitary cuspidal automorphic representation of some general linear group and b is an integer. In this paper, we 更新日期：2020-06-15 • Math. Z. (IF 0.881) Pub Date : 2020-06-15 Christy Hazel A surface with an involution can be viewed as a $$C_2$$-space where $$C_2$$ is the cyclic group of order two. Up to equivariant isomorphism, all involutions on surfaces were classified in Bujalance et al. (Math Z 211:461–478, 1992) and recently classified using equivariant surgery in Dugger (J Homotopy Relat Struct 14(4):919–992, 2019). We use the classification given in Dugger (2019) to compute the 更新日期：2020-06-15 • Math. Z. (IF 0.881) Pub Date : 2020-06-13 David Hansen, Shizhang Li We prove several related results on the low-degree Hodge numbers of proper smooth rigid analytic varieties over non-archimedean fields. Our arguments rely on known structure theorems for the relevant Picard varieties, together with recent advances in p-adic Hodge theory. We also define a rigid analytic Albanese naturally associated with any smooth proper rigid space. 更新日期：2020-06-13 • Math. Z. (IF 0.881) Pub Date : 2020-06-10 Alex Fink, Karola Mészáros, Avery St. Dizier We prove that if $$\sigma \in S_m$$ is a pattern of $$w \in S_n$$, then we can express the Schubert polynomial $$\mathfrak {S}_w$$ as a monomial times $$\mathfrak {S}_\sigma$$ (in reindexed variables) plus a polynomial with nonnegative coefficients. This implies that the set of permutations whose Schubert polynomials have all their coefficients equal to either 0 or 1 is closed under pattern containment 更新日期：2020-06-10 • Math. Z. (IF 0.881) Pub Date : 2020-06-09 Boris Doubrov, Alexandr Medvedev, Dennis The We classify all (locally) homogeneous Levi non-degenerate real hypersurfaces in $${{\mathbb {C}}}^3$$ with symmetry algebra of dimension $$\ge 6$$. 更新日期：2020-06-09 • Math. Z. (IF 0.881) Pub Date : 2020-06-08 Daniel Barlet, Teresa Monteiro Fernandes We introduce new complex analytic integral transforms, the Lisbon Integrals, which naturally arise in the study of the affine space $$\mathbb {C}^k$$ of unitary polynomials $$P_s(z)$$ where $$s\in \mathbb {C}^k$$ and $$z\in \mathbb {C}$$, $$s_i$$ identified to the i-th symmetric function of the roots of $$P_s(z)$$. We completely determine the $$\mathscr {D}$$-modules (or systems of partial differential 更新日期：2020-06-08 • Math. Z. (IF 0.881) Pub Date : 2020-06-08 Shih-Yu Chen We prove an equality between the gamma factors for the Asai cube representation of $$\mathrm{R}_{E/F}\mathrm{{GL}}_2$$ defined by the Weil–Deligne representations and by the local zeta integrals of Ikeda and Piatetski-Shapiro–Rallis, where E is an étale cubic algebra over a local field F of characteristic zero. 更新日期：2020-06-08 • Math. Z. (IF 0.881) Pub Date : 2020-06-05 Allan Greenleaf, Alex Iosevich, Sevak Mkrtchyan We prove the existence of similar and multi-similar point configurations (or simplexes) in sets of fractional Hausdorff dimension in Euclidean space. Let $$d \ge 2$$ and $$E\subset {{{\mathbb {R}}} }^d$$ be a compact set. For $$k\ge 1$$, define\begin{aligned} \Delta _k(E)=\left\{ \left( |x^1-x^2|, \dots , |x^i-x^j|,\dots , |x^k-x^{k+1}|\right) : \left\{ x^i\right\} _{i=1}^{k+1}\subset E\right\}

更新日期：2020-06-05
• Math. Z. (IF 0.881) Pub Date : 2020-06-05
Dongwen Liu, Zhicheng Wang

In this paper we study the Gan–Gross–Prasad problem for unitary groups over finite fields. Our results provide complete answers for unipotent representations, and we obtain the explicit branching of these representations.

更新日期：2020-06-05
• Math. Z. (IF 0.881) Pub Date : 2020-06-05
T. Anderson, K. Hughes, J. Roos, A. Seeger

Let $$f\in L^p({\mathbb {R}}^d)$$, $$d\ge 3$$, and let $$A_t f(x)$$ be the average of f over the sphere with radius t centered at x. For a subset E of [1, 2] we prove close to sharp $$L^p\rightarrow L^q$$ estimates for the maximal function $$\sup _{t\in E} |A_t f|$$. A new feature is the dependence of the results on both the upper Minkowski dimension of E and the Assouad dimension of E. The result

更新日期：2020-06-05
• Math. Z. (IF 0.881) Pub Date : 2020-06-05
Sondre Kvamme

For an exact category $${{\mathcal {E}}}$$ with enough projectives and with a $$d\mathbb {Z}$$-cluster tilting subcategory, we show that the singularity category of $${{\mathcal {E}}}$$ admits a $$d\mathbb {Z}$$-cluster tilting subcategory. To do this we introduce cluster tilting subcategories of left triangulated categories, and we show that there is a correspondence between cluster tilting subcategories

更新日期：2020-06-05
• Math. Z. (IF 0.881) Pub Date : 2020-06-04
Sheng Rao, Yongpan Zou

We give a new Tian–Todorov lemma on deformations of CR-structures and use it to reprove the deformation unobstructedness of normal compact strongly pseudoconvex CR-manifold under the assumption of $$d'd''$$-lemma, more faithfully following Tian–Todorov’s approach.

更新日期：2020-06-04
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