A Converse Theorem for Split SO2l over Finite Fields

被引：0

作者：

Alexander Hazeltine

Bai Ying Liu

机构：

[1] Purdue University,Department of Mathematics

来源：

Acta Mathematica Sinica, English Series | 2024年 / 40卷

关键词：

Converse theorems; generic cuspidal representations; even special orthogonal groups; 20C33; 20G40;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We prove a converse theorem for split even special orthogonal groups over finite fields. This is the only case left on converse theorems of classical groups and the difficulty is the existence of the outer automorphism. In this paper, we develop new ideas and overcome this difficulty.

引用

页码：731 / 771

页数：40

共 50 条

[41] Twists, Euler products and a converse theorem for L-functions of degree 2
Kaczorowski, Jerzy
Perelli, Alberto
ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2015, 14 (02) : 441 - 480
[42] On the L-polynomials of curves over finite fields
Ballini, Francesco
Lombardo, Davide
Verzobio, Matteo
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2025,
[43] AN L2-ISOLATION THEOREM FOR YANG-MILLS FIELDS OVER COMPLETE MANIFOLDS
DODZIUK, J
MINOO
COMPOSITIO MATHEMATICA, 1982, 47 (02) : 165 - 169
[44] SERRE'S THEOREM AND MEASURES CORRESPONDING TO ABELIAN VARIETIES OVER FINITE FIELDS
Tsfasman, Michael A.
MOSCOW MATHEMATICAL JOURNAL, 2019, 19 (04) : 789 - 806
[45] Algebraic groups over finite fields, a quick proof of Lang's theorem
Müller, P
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 131 (02) : 369 - 370
[46] A GOLDBACH THEOREM FOR POLYNOMIALS OF LOW DEGREE OVER ODD FINITE-FIELDS
EFFINGER, G
ACTA ARITHMETICA, 1983, 42 (04) : 329 - 365
[47] Brauer-Siegel Theorem for Families of Elliptic Surfaces over Finite Fields
Zykin, A. I.
MATHEMATICAL NOTES, 2009, 86 (1-2) : 140 - 142
[48] DUALITY THEOREM FOR FINITE COMMUTATIVE GROUP ARRAYS OVER CONGRUENCE FUNCTION FIELDS
FREY, G
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1978, 301 : 46 - 58
[49] Brauer-Siegel theorem for families of elliptic surfaces over finite fields
A. I. Zykin
Mathematical Notes, 2009, 86 : 140 - 142
[50] A detailed description of the binomial theorem and an application to permutation binomials over finite fields
Zhilin Zhang
Lang Tang
Ningjing Huang
Journal of Applied Mathematics and Computing, 2022, 68 : 177 - 198

← 1 2 3 4 5 →