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Related papers: Non-vanishing of certain integral representations

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Following the approach of B. Roberts, we characterize the non-vanishing of global theta lifts for symplectic-orthogonal dual pairs in terms of its local counterpart. In particular, we replace the temperedness assumption present in Robert's…

Number Theory · Mathematics 2010-05-13 Shuichiro Takeda

We are concerned with the two-power nonlinear Schr\"odinger-type equations with non-local terms. We consider the framework of Sobolev-Lorentz spaces which contain singular functions with infinite-energy. Our results include global…

Analysis of PDEs · Mathematics 2019-10-02 Vanessa Barros , Lucas C. F. Ferreira , Ademir Pastor

The exponential localization of Wannier functions in two or three dimensions is proven for all insulators that display time-reversal symmetry, settling a long-standing conjecture. Our proof relies on the equivalence between the existence of…

In this note we review some recent results concerning integral representation properties of local functionals driven by Lipschitz continuous anisotropies.

Analysis of PDEs · Mathematics 2025-09-16 Simone Verzellesi

In this paper a special class of local zeta functions is studied. The main theorem states that the functions have all zeros on the line Re (s)=1/2. This is a natural generalization of the result of Bump and Ng stating that the zeros of the…

Number Theory · Mathematics 2007-05-23 Rikard Olofsson

In this article, we study (simultaneous) non-vanishing, (simultaneous) sign changes of Fourier coefficients of (two) Hilbert cusp forms, respectively.

Number Theory · Mathematics 2021-12-10 Narasimha Kumar , Tarun Dalal

We prove vanishing of distribution on p-adic spherical spaces that are equivariant with respect to a generic character of the nilradical of a Borel subgroup and satisfy a certain condition on the wave-front set. We deduce from this…

Representation Theory · Mathematics 2016-05-06 Avraham Aizenbud , Dmitry Gourevitch , Alexander Kemarsky

We identify type-preserving representations $\phi: \pi_1(\Sigma)\to \mathrm{PSL}(2,\mathbb{R})$ of the fundamental group of every punctured surface $\Sigma = \Sigma_{g,p}$ that are not Fuchsian yet send all non-peripheral simple closed…

Geometric Topology · Mathematics 2025-11-19 Inyoung Ryu

We investigate differentiability of functions defined on regions of the real quaternion field and obtain a noncommutative version of the Cauchy-Riemann conditions. Then we study the noncommutative analog of the Cauchy integral as well as…

Complex Variables · Mathematics 2007-05-23 S. V. Ludkovsky , F. van Oystaeyen

We prove the non-vanishing of special $L$-values of cuspidal automorphic forms on GL(2) twisted by Hecke characters of prime power orders and totally split prime power conductors. Main ingredients of the proof are estimating the Galois…

Number Theory · Mathematics 2021-01-26 Jaesung Kwon , Hae-Sang Sun

We show that every linear functional on the Dirichlet space that is non-zero on nowhere-vanishing functions is necessarily a multiple of a point evaluation. Continuity of the functional is not assumed. As an application, we obtain a…

Functional Analysis · Mathematics 2019-02-13 Javad Mashreghi , Julian Ransford , Thomas Ransford

In a previous article we had proved an algebraicity result for the central critical value for L-functions for GL(n) x GL(n-1) over Q assuming the validity of a nonvanishing hypothesis involving archimedean integrals. The purpose of this…

Number Theory · Mathematics 2015-03-05 A. Raghuram

In this paper, we study harmonic and caloric functions of polynomial growth on a complete non-compact gradient shrinking Ricci soliton. On one hand, when the scalar curvature satisfies at least quadratic decay, we prove that the space of…

Differential Geometry · Mathematics 2023-07-12 Jia-Yong Wu , Peng Wu

In this review article we present regularity properties of generalized functions which are useful in the analysis of non-linear problems. It is shown that Schwartz distributions embedded into our new spaces of generalized functions, with…

Functional Analysis · Mathematics 2014-07-25 Stevan Pilipovic , Dimitris Scarpalezos , Jasson Vindas

We review several properties of integrals of the Wigner distribution on subsets of the phase space. Along our way, we provide a theoretical proof of the invalidity of Flandrin's conjecture, a fact already proven via numerical arguments in…

Spectral Theory · Mathematics 2023-02-28 Nicolas Lerner

No functions class for general measurable sets classes are known whose functions have the property of differentiability of integrals associated to such sets classes. In this paper,we give some subspaces of $L^s$ with $1<s<\infty$, whose…

Classical Analysis and ODEs · Mathematics 2014-07-09 Shunchao Long

This paper considers the family of Schr\"odinger operators on $\ell^2(\mathbb{Z})$ given by independent but not necessarily identically distributed and possibly unbounded potentials. We assume a finite exponential moment and allow the…

Mathematical Physics · Physics 2026-04-03 Karl Zieber

A `locally-finite' observable is one for which there is no region of divergence anywhere in the space of real loop momenta; it can therefore be computed (in principle) without regularization. In this work, we prove that all two-loop ratio…

High Energy Physics - Theory · Physics 2021-05-19 Jacob L. Bourjaily , Cameron Langer , Kokkimidis Patatoukos

The nonvanishing problem asks if a coefficient of a polynomial is nonzero. Many families of polynomials in algebraic combinatorics admit combinatorial counting rules and simultaneously enjoy having saturated Newton polytopes (SNP). Thereby,…

Combinatorics · Mathematics 2021-03-09 Anshul Adve , Colleen Robichaux , Alexander Yong

We generalize the Bartsch-Li's splitting lemma at infinity for $C^2$-functionals in [2] and some later variants of it to a class of continuously directional differentiable functionals on Hilbert spaces. Different from the previous flow…

Functional Analysis · Mathematics 2015-01-27 Guangcun Lu