On values of the Bessel function for generic representations of finite general linear groups

DOI10.1016/j.aim.2023.109314arXiv2211.03678MaRDI QIDQ6065298

Elad Zelingher

Publication date: 14 November 2023

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2211.03678

zbMATH Keywords

Kloosterman sumsBessel functionsKloosterman sheaves

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Gauss and Kloosterman sums; generalizations (11L05) Other character sums and Gauss sums (11T24) Representations of finite groups of Lie type (20C33)

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Cites Work

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• New equidistribution estimates of Zhang type
• Zeta functions attached to finite general linear groups
• Explicit Shintani base change and the Macdonald correspondence for characters of GL\(_n(k)\)
• Darstellungen von \(GL(3,F_ q)\) und Gaußsche Summen
• Two remarks on irreducible characters of finite general linear groups
• Cohomologie étale. Seminaire de géométrie algébrique du Bois-Marie SGA 4 1/2 par P. Deligne, avec la collaboration de J. F. Boutot, A. Grothendieck, L. Illusie et J. L. Verdier
• Unitary Kloosterman sums and the Gelfand-Graev representation of \(GL_2\)
• Functoriality for the classical groups
• Kloosterman sheaves for reductive groups
• Transfer operators and Hankel transforms between relative trace formulas. I: Character theory
• Harmonic analysis on \(\mathrm{GL}_n\) over finite fields
• Exterior square gamma factors for cuspidal representations of \(GL_n\): finite field analogs and level-zero representations
• Epsilon factors of representations of finite general linear groups
• Converse theorem of Gauss sums. With an appendix by Zhiwei Yun
• \(n\times 1\) local gamma factors and Gauss sums
• Bilinear forms with Kloosterman sums and applications
• Rankin-Selberg gamma factors of level zero representations of \(\mathrm{GL}_{n}\)
• Bessel functions and local converse conjecture of Jacquet
• Cuspidal Modules as Summands of a Gel'fand–Graev Module
• The Characters of the Finite General Linear Groups
• REPRESENTATIONS OF THE HECKE ALGEBRA FOR GL₄(q)
• On the realization of maximal simple types and epsilon factors of pairs
• The Lee‐Yang and Pólya‐Schur programs. II. Theory of stable polynomials and applications
• Complex Representations of 𝐺𝐿(2,𝐾) for Finite Fields 𝐾
• Fourier Transforms of Intertwining Operators and Plancherel Measures for GL(n)
• Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116)
• Cuspidal Matrix Representations for GL₂ (q ) and GL₃ (q )
• Estimates for Soto-Andrade sums.
• On an explicit formula for class-$1$ “Whittaker functions” on $GL_n $ over $\beta $-adic fields
• The Cuspidal Modules of the Finite General Linear Groups
• The characters of the generalized Steinberg representations of finite general linear groups on the regular elliptic set
• Stratification and averaging for exponential sums: bilinear forms with generalized Kloosterman sums
• A proof of the finite field analogue of Jacquet’s conjecture
• REPRESENTATIONS OF THE FULL LINEAR GROUP OVER A FINITE FIELD
• L-functions for symmetric products of Kloosterman sums
• Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model