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Global $$\textbf{B}(G)$$ with adelic coefficients and transfer factors at non-regular elements Math. Z. (IF 0.8) Pub Date : 2024-03-15 Alexander Bertoloni Meli
The goal of this paper is extend Kottwitz’s theory of B(G) for global fields. In particular, we show how to extend the definition of “B(G) with adelic coefficients” from tori to all connected reductive groups. As an application, we give an explicit construction of certain transfer factors for non-regular semisimple elements of non-quasisplit groups. This generalizes some results of Kaletha and Taibi
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Ill-posedness for the Half wave Schrödinger equation Math. Z. (IF 0.8) Pub Date : 2024-03-15 Isao Kato
We study the Cauchy problem for the half wave Schrödinger equation introduced by Xu [9]. There are some well-posedness results for the equation, however there is no ill-posedness result. We focus on the scale critical space and obtain the ill-posedness in the super-critical or at the critical space under certain condition. The proofs in the super-critical space are based on the argument established
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Bloom weighted bounds for sparse forms associated to commutators Math. Z. (IF 0.8) Pub Date : 2024-03-15 Andrei K. Lerner, Emiel Lorist, Sheldy Ombrosi
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Jordan mating is always possible for polynomials Math. Z. (IF 0.8) Pub Date : 2024-03-15
Abstract Suppose f and g are two post-critically finite polynomials of degree \(d_1\) and \(d_2\) respectively and suppose both of them have a finite super-attracting fixed point of degree \(d_0\) . We prove that one can always construct a rational map R of degree $$\begin{aligned} D = d_1 + d_2 - d_0 \end{aligned}$$ by gluing f and g along the Jordan curve boundaries of the immediate super-attracting
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D-finiteness, rationality, and height III: multivariate Pólya–Carlson dichotomy Math. Z. (IF 0.8) Pub Date : 2024-03-14 Jason P. Bell, Shaoshi Chen, Khoa D. Nguyen, Umberto Zannier
We prove a result that can be seen as an analogue of the Pólya–Carlson theorem for multivariate D-finite power series with coefficients in \(\bar{\mathbb {Q}}\). In the special case that the coefficients are algebraic integers, our main result says that if $$\begin{aligned} F(x_1,\ldots ,x_m)=\sum f(n_1,\ldots ,n_m)x_1^{n_1}\cdots x_m^{n_m} \end{aligned}$$ is a D-finite power series in m variables
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Cohomology and geometry of Deligne–Lusztig varieties for $$\textrm{GL}_n$$ Math. Z. (IF 0.8) Pub Date : 2024-03-14 Yingying Wang
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Matrix Kloosterman sums modulo prime powers Math. Z. (IF 0.8) Pub Date : 2024-03-14 M. Erdélyi, Á. Tóth, G. Zábrádi
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A note on the semistability of singular projective hypersurfaces Math. Z. (IF 0.8) Pub Date : 2024-03-14 Thomas Mordant
In this note, we give sufficient conditions for the (semi)stability of a hypersurface H of \(\mathbb {P}^N_k\) in terms of its degree d, the maximal multiplicity \(\delta \) of its singularities, and the dimension s of its singular locus. For instance, we show that H is semistable when \(d \ge \delta \min (N+1, s+3)\). The proof relies in particular on Benoist’s lower bound for the dimension of the
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Canonical integral operators on the Fock space Math. Z. (IF 0.8) Pub Date : 2024-03-12 Xingtang Dong, Kehe Zhu
In this paper we introduce and study a two-parameter family of integral operators on the Fock space \(F^2({\mathbb {C}})\). We determine exactly when these operators are bounded and when they are unitary. We show that, under the Bargmann transform, these operators include the classical linear canonical transforms as special cases. As an application, we obtain a new unitary projective representation
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Nonempty interior of configuration sets via microlocal partition optimization Math. Z. (IF 0.8) Pub Date : 2024-03-12 Allan Greenleaf, Alex Iosevich, Krystal Taylor
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Whittaker categories and the minimal nilpotent finite W-algebras for $$\mathfrak {sl}_{n+1}$$ Math. Z. (IF 0.8) Pub Date : 2024-03-12 Genqiang Liu, Yang Li
For any \({\textbf{a}}=(a_1,\dots ,a_n)\in {\mathbb {C}}^n\), we introduce a Whittaker category \({\mathcal {H}}_{{\textbf{a}}}\) whose objects are \(\mathfrak {sl}_{n+1}\)-modules M such that \(e_{0i}-a_i\) acts locally nilpotently on M for all \(i \in \{1,\dots ,n\}\), and the subspace \(\textrm{wh}_{{\textbf{a}}}(M)=\{v\in M \mid e_{0i} v=a_iv, \ i=1,\dots ,n\}\) is finite dimensional. In this paper
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$$L^{\vec {p}}-L^{\vec {q}}$$ boundedness of multiparameter Forelli–Rudin type operators on the product of unit balls of $${\mathbb {C}}^n$$ Math. Z. (IF 0.8) Pub Date : 2024-03-09 Long Huang, Xiaofeng Wang, Zhicheng Zeng
In this work, we provide a complete characterization of the boundedness of two classes of multiparameter Forelli–Rudin type operators from one mixed-norm Lebesgue space \(L^{{\vec {p}}}\) to another space \(L^{{\vec {q}}}\), when \(1\le \vec {p}\le {\vec {q}}<\infty \), equipped with possibly different weights. Using these characterizations, we establish the necessary and sufficient conditions for
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Rank-one perturbations and norm-attaining operators Math. Z. (IF 0.8) Pub Date : 2024-03-08
Abstract The main goal of this article is to show that for every (reflexive) infinite-dimensional Banach space X there exists a reflexive Banach space Y and \(T, R \in \mathcal {L}(X,Y)\) such that R is a rank-one operator, \(\Vert T+R\Vert >\Vert T\Vert \) but \(T+R\) does not attain its norm. This answers a question posed by Dantas and the first two authors. Furthermore, motivated by the parallelism
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Greatest common divisors for polynomials in almost units and applications to linear recurrence sequences Math. Z. (IF 0.8) Pub Date : 2024-03-08
Abstract We bound the greatest common divisor of two coprime multivariable polynomials evaluated at algebraic numbers, generalizing work of Levin, and going towards conjectured inequalities of Silverman and Vojta. As an application, we prove results on greatest common divisors of terms from two linear recurrence sequences, extending the results of Levin, who considered the case where the linear recurrences
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On inverted Kloosterman sums over finite fields Math. Z. (IF 0.8) Pub Date : 2024-03-07 Xin Lin, Daqing Wan
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The jump problem for the critical Besov space Math. Z. (IF 0.8) Pub Date : 2024-03-07 Tailiang Liu, Yuliang Shen
We introduce the critical Besov space \( B_{p} \) on quasicircles and prove the solvability of the jump problem on d-regular quasicircles with \( B_{p} \) boundary values for \( d
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Fox–Neuwirth cells, quantum shuffle algebras, and the homology of type-B Artin groups Math. Z. (IF 0.8) Pub Date : 2024-03-06 Anh Trong Nam Hoang
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Global endpoint regularity estimates for the fractional Dirichlet problem Math. Z. (IF 0.8) Pub Date : 2024-03-06 Wenxian Ma, Sibei Yang
Let \(n\ge 2\), \(s\in (0,1)\), and \(\Omega \subset {\mathbb {R}}^n\) be a bounded \(C^2\) domain. The aim of this paper is to study the global endpoint regularity estimates for the fractional Dirichlet problem $$\begin{aligned} {\left\{ \begin{array}{ll} (-\Delta )^su=f \ \ {} &{} \text {in}\ \ \Omega ,\\ u=0 \ \ {} &{} \text {in}\ \ {\mathbb {R}}^n\setminus \Omega . \end{array}\right. } \end{aligned}$$
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Generic vanishing, 1-forms, and topology of Albanese maps Math. Z. (IF 0.8) Pub Date : 2024-02-27 Yajnaseni Dutta, Feng Hao, Yongqiang Liu
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Quaternionic slice regularity beyond slice domains Math. Z. (IF 0.8) Pub Date : 2024-02-26 Riccardo Ghiloni, Caterina Stoppato
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Refinements to the prime number theorem for arithmetic progressions Math. Z. (IF 0.8) Pub Date : 2024-02-20 Jesse Thorner, Asif Zaman
We prove a version of the prime number theorem for arithmetic progressions that is uniform enough to deduce the Siegel–Walfisz theorem, Hoheisel’s asymptotic for intervals of length \(x^{7/12+\varepsilon }\), a Brun–Titchmarsh bound, and Linnik’s bound on the least prime in an arithmetic progression as corollaries. Our proof uses the Vinogradov–Korobov zero-free region, a log-free zero density estimate
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$$\ell ^1$$ -summability and Fourier series of B-splines with respect to their knots Math. Z. (IF 0.8) Pub Date : 2024-02-17 Martin Buhmann, Janin Jäger, Yuan Xu
We study the \(\ell ^1\)-summability of functions in the d-dimensional torus \({{\mathbb {T}}}^d\) and so-called \(\ell ^1\)-invariant functions. Those are functions on the torus whose Fourier coefficients depend only on the \(\ell ^1\)-norm of their indices. Such functions are characterized as divided differences that have \(\cos {\theta }_1,\ldots ,\cos {\theta }_d\) as knots for \(({\theta }_1\
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Multiple normalized solutions for the planar Schrödinger–Poisson system with critical exponential growth Math. Z. (IF 0.8) Pub Date : 2024-02-16 Sitong Chen, Vicenţiu D. Rădulescu, Xianhua Tang
The paper deals with the existence of normalized solutions for the following Schrödinger–Poisson system with \(L^2\)-constraint: $$\begin{aligned} \left\{ \begin{array}{ll} -\Delta u+\lambda u+\mu \left( \log |\cdot |*u^2\right) u=\left( e^{u^2}-1-u^2\right) u, &{} x\in {\mathbb {R}}^2, \\ \int _{{\mathbb {R}}^2}u^2\textrm{d}x=c, \\ \end{array} \right. \end{aligned}$$ where \(\mu >0\), \(\lambda \in
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Talbot effect on the sphere and torus for $$d\ge 2$$ Math. Z. (IF 0.8) Pub Date : 2024-02-16 M. Burak Erdoğan, Chi N. Y. Huynh, Ryan McConnell
We utilize exponential sum techniques to obtain upper and lower bounds for the fractal dimension of the graph of solutions to the linear Schrödinger equation on \(\mathbb {S}^d\) and \(\mathbb {T}^d\). Specifically for \(\mathbb S^d\), we provide dimension bounds using both \(L^p\) estimates of Littlewood-Paley blocks, as well as assumptions on the Fourier coefficients. In the appendix, we present
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Isometries in the symmetrized bidisc Math. Z. (IF 0.8) Pub Date : 2024-02-16 Armen Edigarian
We provide a characterization of isometries in the sense of the Carathéodory–Reiffen metric in the symmetrized bidisc.
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Rational points on generic marked hypersurfaces Math. Z. (IF 0.8) Pub Date : 2024-02-14 Qixiao Ma
Over fields of characteristic zero, we show that for \(n=1,d\ge 4\) or \(n=2,d\ge 5\) or \(n\ge 3, d\ge 2n\), the generic m-marked degree-d hypersurface in \(\mathbb {P}^{n+1}\) admits the m marked points as all the rational points. Over arbitrary fields, we show that for \(n=1,d\ge 4\) or \(n\ge 2, d\ge 2n+3\), the identity map is the only rational self-map of the generic degree-d hypersurface in
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Desingularization of binomial varieties using toric Artin stacks Math. Z. (IF 0.8) Pub Date : 2024-02-14 Dan Abramovich, Bernd Schober
We show how the notion of fantastacks can be used to effectively desingularize binomial varieties defined over algebraically closed fields. In contrast to a desingularization via blow-ups in smooth centers, we drastically reduce the number of steps and the number of charts appearing along the process. Furthermore, we discuss how our considerations extend to a partial simultaneous normal crossings desingularization
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Positivity of extensions of vector bundles Math. Z. (IF 0.8) Pub Date : 2024-02-13
Abstract In this paper, we study when positivity conditions of vector bundles are preserved by extension. We prove that an extension of a big (resp. pseudo-effective) line bundle by an ample (resp. a nef) vector bundle is big (resp. pseudo-effective). We also show that an extension of an ample line bundle by a big line bundle is not necessarily pseudo-effective. In particular, this implies that an
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K-theory of relative group $$C^*$$ -algebras and the relative Novikov conjecture Math. Z. (IF 0.8) Pub Date : 2024-02-12 Jintao Deng, Geng Tian, Zhizhang Xie, Guoliang Yu
The relative Novikov conjecture states that the relative higher signatures of manifolds with boundary are invariant under orientation-preserving homotopy equivalences of pairs. The relative Baum–Connes assembly encodes information about the relative higher index of elliptic operators on manifolds with boundary. In this paper, we study the relative Baum–Connes assembly map for any pair of groups and
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Parabolic John–Nirenberg spaces with time lag Math. Z. (IF 0.8) Pub Date : 2024-02-12 Kim Myyryläinen, Dachun Yang
We introduce a parabolic version of the so-called John–Nirenberg space that is a generalization of functions of parabolic bounded mean oscillation. Parabolic John–Nirenberg inequalities, which give weak type estimates for the oscillation of a function, are shown in the setting of the parabolic geometry with a time lag. Our arguments are based on a parabolic Calderón–Zygmund decomposition and a good
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Almost nonnegative Ricci curvature and new vanishing theorems for genera Math. Z. (IF 0.8) Pub Date : 2024-02-10 Xiaoyang Chen, Jian Ge, Fei Han
We derive new vanishing theorems for genera under almost nonnegative Ricci curvature and infinite fundamental group. A vanishing theorem of Euler characteristic number for almost nonnegatively curved Alexandrov spaces is also proved.
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On the distribution of modular square roots of primes Math. Z. (IF 0.8) Pub Date : 2024-02-10 Ilya D. Shkredov, Igor E. Shparlinski, Alexandru Zaharescu
We use recent bounds on bilinear sums with modular square roots to study the distribution of solutions to congruences \(x^2 \equiv p \pmod q\) with primes \(p\leqslant P\) and \(q \leqslant Q\). This can be considered as a combined scenario of Duke, Friedlander and Iwaniec with averaging only over the modulus q and of Dunn, Kerr, Shparlinski and Zaharescu with averaging only over p.
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Quasisymmetric maps, shears, lambda lengths and flips Math. Z. (IF 0.8) Pub Date : 2024-02-09 Hugo Parlier, Dragomir Šarić
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Gradient estimate for solutions of the equation $$\Delta _pv +av^{q}=0$$ on a complete Riemannian manifold Math. Z. (IF 0.8) Pub Date : 2024-02-09
Abstract In this paper, we use the Nash–Moser iteration method to study the local and global behaviors of positive solutions to the nonlinear elliptic equation \(\Delta _pv +av^{q}=0\) defined on a complete Riemannian manifolds (M, g) where \(p>1\) , a and q are constants and \(\Delta _p(v)=\textrm{div}(|\nabla v|^{p-2}\nabla v)\) is the p-Laplace operator. Under some assumptions on a, p and q, we
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Calderón–Zygmund estimates for the fully nonlinear obstacle problem with super-linear Hamiltonian terms and unbounded ingredients Math. Z. (IF 0.8) Pub Date : 2024-02-09 João Vitor da Silva, Romário Tomilhero Frias
In this work, we show the existence/uniqueness of \(L^p\)-viscosity solutions for a fully non-linear obstacle problem with super-linear gradient growth, unbounded ingredients and irregular obstacles. In our results, we obtain Calderón–Zygmund estimates, namely \(W^{2,p}_{loc}\) regularity estimates (with \(p \in \left( \frac{n}{2}, \infty \right) \)) for such solution. Our findings are newsworthy even
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Maximal functions associated to a family of flat curves in lacunary directions Math. Z. (IF 0.8) Pub Date : 2024-02-08
Abstract Consider the maximal operator defined by $$\begin{aligned} \mathcal {M}^{\mathfrak {a}}_{\gamma }f(x_1,x_2)=\sup _{k\in \mathbb {Z}}\sup _{r>0}\frac{1}{2r}\int _{-r}^{r}|f(x_1-t,x_2-a_k\gamma (t))|dt, \end{aligned}$$ where \(\{(t,\gamma (t))\}\) is a convex curve and \(\mathfrak {a}=(a_k)\) is a lacunary sequence. We observe that \(\gamma '\) doubling assumption does not imply to the \(L^p\)
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Revisit on Heisenberg uniqueness pair for the hyperbola Math. Z. (IF 0.8) Pub Date : 2024-02-08 Debkumar Giri, Ramesh Manna
Let \(\Gamma \) be the hyperbola \(\{(x,y)\in \mathbb {R}^2:xy=1\}\) and \(\Lambda _{\alpha , \beta ,\theta _1, \theta _2}\) be the perturbed lattice-cross defined by \(\Lambda _{\alpha , \beta , \theta _1, \theta _2}=\left( (\alpha \mathbb Z+\{\theta _1\})\times \{0\}\right) \cup \left( \{0\}\times (\beta \mathbb Z+\{\theta _2\})\right) \) in \(\mathbb {R}^2\), where \(\theta _1, \theta _2\in \mathbb
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Zeta functions in higher Teichmüller theory Math. Z. (IF 0.8) Pub Date : 2024-02-06 Mark Pollicott, Richard Sharp
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Marked boundary rigidity for surfaces of Anosov type Math. Z. (IF 0.8) Pub Date : 2024-02-03 Alena Erchenko, Thibault Lefeuvre
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An asymptotic expansion of (k, c)-functions for $$\textrm{GL}_{n}(F)$$ Math. Z. (IF 0.8) Pub Date : 2024-01-30
Abstract Given the important role an asymptotic expansion of Whittaker functions or Shalika functions plays in the study of L-functions via the Rankin–Selberg method, we first establish an asymptotic expansion of (k, c)-functions for \(\textrm{GL}_{n}(F)\) over a p-adic field F via Casselman–Shalika’s argument. As an application, we then show the holomorphy of Ginzburg–Kaplan’s local “tensor product”
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A degeneration approach to Skoda’s division theorem Math. Z. (IF 0.8) Pub Date : 2024-01-29 Roberto Albesiano
We prove a Skoda-type division theorem via a degeneration argument. The proof is inspired by B. Berndtsson and L. Lempert’s approach to the \(L^2\) extension theorem and is based on positivity of direct image bundles. The same tools are then used to slightly simplify and extend the proof of the \(L^2\) extension theorem given by Berndtsson and Lempert.
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The Dixmier–Douady class, the action homomorphism, and group cocycles on the symplectomorphism group Math. Z. (IF 0.8) Pub Date : 2024-01-27 Shuhei Maruyama
Let X be a one-connected and integral symplectic manifold. In this paper, we construct and study a two-cocycle and three-cocycle on the symplectomorphism group of X. In particular, by using these cocycles, we clarify the relationship between Weinstein’s action homomorphism and the universal Dixmier–Douady class of foliated symplectic fibrations.
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On the Bogomolov–Gieseker inequality for tame Deligne–Mumford surfaces Math. Z. (IF 0.8) Pub Date : 2024-01-19 Yunfeng Jiang, Promit Kundu
We generalize the Bogomolov–Gieseker inequality for semistable coherent sheaves on smooth projective surfaces to smooth Deligne–Mumford surfaces. We work over positive characteristic \(p>0\) and generalize Langer’s method to smooth Deligne–Mumford stacks. As applications we obtain the Bogomolov inequality for semistable coherent sheaves on a Deligne–Mumford surface in characteristic zero, and the Bogomolov
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Two-step nilpotent extensions are not anabelian Math. Z. (IF 0.8) Pub Date : 2024-01-19
Abstract We prove the existence of two non-isomorphic number fields K and L such that the maximal two-step nilpotent quotients of their absolute Galois groups are isomorphic. In particular, one may take K and L to be any of the fields \({\mathbb {Q}}(\sqrt{-11})\) , \({\mathbb {Q}}(\sqrt{-19})\) , \({\mathbb {Q}}(\sqrt{-43})\) , \({\mathbb {Q}}(\sqrt{-67})\) or \({\mathbb {Q}}(\sqrt{-163})\) . Furthermore
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The topological shadow of $${{{\mathbb {F}}}_1}$$ -geometry: congruence spaces Math. Z. (IF 0.8) Pub Date : 2024-01-18 Oliver Lorscheid, Samarpita Ray
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On existence of solutions for some classes of elliptic problems with supercritical exponential growth Math. Z. (IF 0.8) Pub Date : 2024-01-18
Abstract In the present paper, we study the existence of solutions for the following classes of elliptic problems where \(\Omega \subset \mathbb {R}^2\) is a smooth bounded domain and where \(V\in C^0(\mathbb {R}^2)\) is periodic in \(\mathbb {Z}^2\) with \(0\not \in \sigma (-\Delta +V)\) . In the both problems above, f is a continuous function of the form $$\begin{aligned} f(t)=h(t)e^{\alpha _0 |t|^\tau
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“The Sierpinski gasket minus its bottom line” as a tree of Sierpinski gaskets Math. Z. (IF 0.8) Pub Date : 2024-01-16 J. Kigami, K. Takahashi
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Syzygies of curves in products of projective spaces Math. Z. (IF 0.8) Pub Date : 2024-01-14 John Cobb
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Addition–deletion theorems for the Solomon–Terao polynomials and B-sequences of hyperplane arrangements Math. Z. (IF 0.8) Pub Date : 2024-01-11 Takuro Abe
We prove the addition–deletion theorems for the Solomon–Terao polynomials, which have two important specializations. Namely, one is to the characteristic polynomials of hyperplane arrangements, and the other to the Poincarè polynomials of the regular nilpotent Hessenberg varieties. One of the main tools to show them is the free surjection theorem which confirms the right exactness of several important
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Automorphic measures and invariant distributions for circle dynamics Math. Z. (IF 0.8) Pub Date : 2024-01-13 Edson de Faria, Pablo Guarino, Bruno Nussenzveig
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Arithmetic purity of strong approximation for complete toric varieties Math. Z. (IF 0.8) Pub Date : 2024-01-11 Sheng Chen
In this article, we establish the arithmetic purity of strong approximation for smooth loci of weighted projective spaces. By using this result and the descent method, we also prove that the arithmetic purity of strong approximation with Brauer–Manin obstruction holds for any smooth and complete toric variety.
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Cr eigenvalue estimate and Kohn-Rossi cohomology II Math. Z. (IF 0.8) Pub Date : 2024-01-11 Zhiwei Wang, Xiangyu Zhou
Let X be a weakly pseudoconvex, compact, and connected CR manifold with a transversal CR \(S^1\)-action of real dimension \(2n-1\), where \(n\ge 2\). The Fourier components of the Kohn-Rossi cohomology, with respect to the \(S^1\)-action, introduced by Hsiao-Li [6], are closely related to the embedding problem of CR manifolds. In this paper, we continue our previous study [14] and provide a sharp estimate
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Stein–Weiss type inequality on the upper half space and its applications Math. Z. (IF 0.8) Pub Date : 2024-01-10 Xiang Li, Zifei Shen, Marco Squassina, Minbo Yang
Abstract In this paper, we establish some Stein–Weiss type inequalities with general kernels on the upper half space and study the extremal functions of the optimal constant. Furthermore, we also investigate the regularity, asymptotic estimates, symmetry and non-existence results of positive solutions of corresponding Euler–Lagrange system. As an application, we derive some Liouville type results for
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Densities on Dedekind domains, completions and Haar measure Math. Z. (IF 0.8) Pub Date : 2024-01-09 Luca Demangos, Ignazio Longhi
Let D be the ring of S-integers in a global field and \({\widehat{D}}\) its profinite completion. Given \(X\subseteq D^n,\) we consider its closure \({\widehat{X}}\subseteq {\widehat{D}}^n\) and ask what can be learned from \({\widehat{X}}\) about the “size” of X. In particular, we ask when the density of X is equal to the Haar measure of \({\widehat{X}}.\) We provide a general definition of density
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The Newlander–Nirenberg Theorem for Principal Bundles Math. Z. (IF 0.8) Pub Date : 2024-01-03 Andrei Teleman
Let G be an arbitrary (not necessarily isomorphic to a closed subgroup of \(\textrm{GL}(r,\mathbb {C})\)) complex Lie group, U a complex manifold and \(p:P\rightarrow U\) a \(\mathcal {C}^\infty \) principal G-bundle on U. We introduce and study the space \(\mathcal {J}^\kappa _P\) of bundle almost complex structures of Hölder class \(\mathcal {C}^\kappa \) on P. To any \(J\in \mathcal {J}^\kappa _P\)
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Hierarchically hyperbolic groups and uniform exponential growth Math. Z. (IF 0.8) Pub Date : 2023-12-20 Carolyn R. Abbott, Thomas Ng, Davide Spriano, Radhika Gupta, Harry Petyt
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On complete space-like stationary surfaces in 4-dimensional Minkowski space with graphical Gauss image Math. Z. (IF 0.8) Pub Date : 2023-12-11 Li Ou, Chuanmiao Cheng, Ling Yang
Concerning the value distribution problem for generalized Gauss maps, we not only generalize Fujimoto’s theorem (J Math Soc Jpn 40:235–247, 1988) to complete space-like stationary surfaces in \(\mathbb {R}^{3,1}\), but also estimate the upper bound of the number of exceptional values when the Gauss image lies in the graph of a rational function f of degree m, which is determined by the number of solutions
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Wall crossing for moduli of stable sheaves on an elliptic surface Math. Z. (IF 0.8) Pub Date : 2023-12-12 Kōta Yoshioka
Bridgeland studied moduli of stable sheaves on elliptic surfaces by using Fourier-Mukai transforms. In this paper, we shall study the wall crossing behavior of the moduli of stable sheaves which is a refinement of Bridgeland’s results.
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Measure upper bounds of nodal sets of Robin eigenfunctions Math. Z. (IF 0.8) Pub Date : 2023-12-08 Fang Liu, Long Tian, Xiaoping Yang
In this paper, we will establish the upper bounds of the Hausdorff measure of nodal sets of eigenfunctions with the Robin boundary conditions, i.e., $$\begin{aligned} {\left\{ \begin{array}{l} \triangle u+\lambda u=0,\quad in\quad \Omega ,\\ u_{\nu }+\mu u=0,\quad on\quad \partial \Omega , \end{array} \right. } \end{aligned}$$ where the domain \(\Omega \subseteq \mathbb {R}^n\), \(u_{\nu }\) is the