Results 51 to 60 of about 702,417 (178)

Doubling constructions and tensor product L-functions: coverings of the symplectic group

Forum of Mathematics, Sigma
In this work, we develop an integral representation for the partial L-function of a pair $\pi \times \tau $ of genuine irreducible cuspidal automorphic representations, $\pi $ of the m-fold covering of Matsumoto of the symplectic group $
Eyal Kaplan
doaj   +1 more source

Small automorphic representations and degenerate Whittaker vectors [PDF]

, 2014
We investigate Fourier coefficients of automorphic forms on split simply-laced Lie groups G. We show that for automorphic representations of small Gelfand-Kirillov dimension the Fourier coefficients are completely determined by certain degenerate ...
H. Gustafsson, A. Kleinschmidt, D. Persson   +2 more
semanticscholar   +1 more source

Distribution of integer points on determinant surfaces and a mod‐p analogue

Mathematika, Volume 72, Issue 2, April 2026.
Abstract We establish an asymptotic formula for counting integer solutions with smooth weights to an equation of the form xy−zw=r$xy-zw=r$, where r$r$ is a non‐zero integer, with an explicit main term and a strong bound on the error term in terms of the size of the variables x,y,z,w$x, y, z, w$ as well as of r$r$.
Satadal Ganguly, Rachita Guria
wiley   +1 more source

Local-global compatibility for regular algebraic cuspidal automorphic representations when $\ell \neq p$

Forum of Mathematics, Sigma
We prove the compatibility of local and global Langlands correspondences for $\operatorname {GL}_n$ up to semisimplification for the Galois representations constructed by Harris-Lan-Taylor-Thorne [10] and Scholze [18]. More precisely, let $r_p(
Ila Varma
doaj   +1 more source

Moments of L$L$‐functions via a relative trace formula

Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.
Abstract We prove an asymptotic formula for the second moment of the GL(n)×GL(n−1)$\mathrm{GL}(n)\times \mathrm{GL}(n-1)$ Rankin–Selberg central L$L$‐values L(1/2,Π⊗π)$L(1/2,\Pi \otimes \pi)$, where π$\pi$ is a fixed cuspidal representation of GL(n−1)$\mathrm{GL}(n-1)$ that is tempered and unramified at every place, while Π$\Pi$ varies over a family of
Subhajit Jana, Ramon Nunes
wiley   +1 more source

Construction of automorphic Galois representations, II [PDF]

Cambridge Journal of Mathematics, 2013
Recent developments in the theory of the stable trace formula, especially the proof by Laumon and Ngo of the fundamental lemma for unitary groups, has revived Langlands’ strategy for constructing Galois representations in the `-adic cohomology of Shimura varieties.
Chenevier, Gaëtan, Harris, Michael
openaire   +3 more sources

Joint distribution of Hecke eigenforms on H3$ \mathbb {H}^3$

Mathematische Nachrichten, Volume 299, Issue 3, Page 661-674, March 2026.
Abstract We prove a joint value equidistribution statement for Hecke–Maaß cusp forms on the hyperbolic three‐space H3$\mathbb {H}^3$. This supports the conjectural statistical independence of orthogonal cusp forms.
Didier Lesesvre, Luca Marchesini, Nicole Raulf   +2 more
wiley   +1 more source

A generalized $\mathrm{PGL}(2)$ Petersson/Bruggeman-Kuznetsov formula for analytic applications

Forum of Mathematics, Sigma
We develop generalized Petersson/Bruggeman-Kuznetsov (PBK) formulas for specified local components at non-archimedean places. In fact, we introduce two hypotheses on non-archimedean test function pairs $f \leftrightarrow \pi (f)$ , called geometric
Yueke Hu, Ian Petrow, Matthew P. Young
doaj   +1 more source

Rigidity of anti‐de Sitter (2+1)‐spacetimes with convex boundary near the Fuchsian locus

Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.
Abstract We prove that globally hyperbolic compact anti‐de Sitter (2+1)‐spacetimes with a strictly convex spacelike boundary that is either smooth or polyhedral and whose holonomy is close to Fuchsian are determined by the induced metric on the boundary.
Roman Prosanov, Jean‐Marc Schlenker
wiley   +1 more source

R4 couplings and automorphic unipotent representations [PDF]

Journal of High Energy Physics, 2010
Four-graviton, eight-derivative couplings in the low energy effective action of toroidal type II string compactifications are tightly constrained by U-duality invariance and by supersymmetry. In this note, we revisit earlier proposals for the automorphic form governing these couplings in dimension D=3,4,5,6, and propose that the correct automorphic ...
openaire   +4 more sources