Finite period vectors and Gauss sums
type: Item
instance of: scholarly article
title: Finite period vectors and Gauss sums
zbMATH Open document ID: 1546.11077
author: Yeongseong Jo
published in: Finite Fields and their Applications
publication date: 2024-07-02T00:00:00Z
review text: In this paper, the author studies four families of sums associated to irreducible cuspidal representations of general linear groups over finite fields, namely, the Jacquet-Piatetski-Shapiro-Shalika, Flicker, Bump-Friedberg, and Jacquet-Shalika sums. For the last three newly explored cases, the corresponding gamma factors are expressed explicitly in terms of Gauss sums. The Asai and Bump-Friedberg gamma factors over finite fields are related to the ones over non-Archimedean local fields via the construction of depth zero supercuspidal representations. It is shown that the exterior square and Bump-Friedberg gamma factors agree with the corresponding Artin gamma factors via local Langlands correspondence and Deligne-Kazhdan close field theory. Finally, the author examines the four families of period and vectors, and their connections to the corresponding gamma factors.
reviewed by: Dongwen Liu
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 11F66
Mathematics Subject Classification ID: 20C33
Mathematics Subject Classification ID: 22E50
Mathematics Subject Classification ID: 11T24
zbMATH DE Number: 7874556
zbMATH Keywords: close field theory
zbMATH Keywords: gamma and epsilon factors
zbMATH Keywords: Gauss sums
zbMATH Keywords: integral representations
zbMATH Keywords: level zero representations
zbMATH Keywords: period vectors and integrals
MaRDI profile type: Publication
cites work: Distinguished representations and poles of twisted tensor 𝐿-functions
cites work: Galois self-dual cuspidal types and Asai local factors
cites work: Test vectors for local periods
cites work: Test vectors for finite periods and base change
cites work: Archimedean Theory and 𝜖-Factors for the Asai Rankin-Selberg Integrals
cites work: Q3497144
cites work: Non-Abelian Congruence Gauss Sums and p -Adic Simple Algebras
cites work: Hereditary orders, Gauss sums and supercuspidal representations of GLN.
cites work: Q5481252
cites work: Local Rankin-Selberg convolutions for 𝐺𝐿_{𝑛}: Explicit conductor formula
cites work: Derivatives and \(L\)-functions for \(\mathrm{GL}_n\)
cites work: Local Langlands correspondence for \(\mathrm{GL}_n\) and the exterior and symmetric square \(\varepsilon\)-factors
cites work: Les Constantes des Equations Fonctionnelles des Fonctions L
cites work: Q3699806
cites work: Restrictions of representations of classical groups: examples
cites work: The local Langlands correspondence for GSp4 over local function fields
cites work: On twisted exterior and symmetric square \(\gamma\)-factors
cites work: Zeta functions of simple algebras
cites work: Q4550395
cites work: Local-to-global extensions for GLn in non-zero characteristic: a characterizat
cites work: Uniqueness of Rankin-Selberg products
cites work: Test vectors for Archimedean period integrals
cites work: Archimedean zeta integrals for the exterior square \(L\)-functions on \(\mathrm{GL}_{n}\)
cites work: Q3470542
cites work: Derivatives and exceptional poles of the local exterior square \(L\)-function for \(\mathrm{GL}_m\)
cites work: Local exterior square and Asai \(L\)-functions for \(\operatorname{GL}(n)\) in odd characteristic
cites work: The local period integrals and essential vectors
cites work: The local exterior square \(L\)-function: holomorphy, non-vanishing and Shalika functionals
cites work: On automorphic \(L\)-functions in positive characteristic
cites work: Distinguished representations and exceptional poles of the Asai \(L\)-function
cites work: Linear and Shalika local periods for the mirabolic group, and some consequences
cites work: On the local Bump-Friedberg \(L\)-function
cites work: On the local Bump-Friedberg \(L\)-function. II
cites work: \(n\times 1\) local gamma factors and Gauss sums
cites work: Gamma factors and quadratic extension over finite fields
cites work: Local gamma factors, converse theorems and related problems
cites work: On local root numbers and distinction
cites work: On the realization of maximal simple types and epsilon factors of pairs
cites work: Multiplicities under basechange: finite field case
cites work: Local coefficients as Artin factors for real groups
cites work: Explicit Shintani base change and the Macdonald correspondence for characters of GL\(_n(k)\)
cites work: On gamma factors for representations of finite general linear groups
cites work: Q6090110
cites work: Rankin-Selberg gamma factors of level zero representations of \(\mathrm{GL}_{n}\)
cites work: Exterior square gamma factors for cuspidal representations of \(GL_n\): finite field analogs and level-zero representations
cites work: Epsilon factors of representations of finite general linear groups
cites work: On values of the Bessel function for generic representations of finite general linear groups
DOI: 10.1016/J.FFA.2024.102443
description: scientific article; zbMATH DE number 7874556