辛群的自同构下降:分支问题与l -函数

IF 1.7 1区数学 Q1 MATHEMATICS

American Journal of Mathematics Pub Date : 2023-05-31 DOI:10.1353/ajm.2023.a897497

Baiying Liu, Bin Xu

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引用次数: 1

摘要

研究了辛群的自同构下降结构，得到了一些与自同构表示的分支问题有关的结果。作为构造的副产物，我们基于${\rm Mp}_2(\Bbb{a})$的全局Vogan包的知识，给出了一个新的方法来证明对于辛型${\rm GL}_2(\Bbb{a})$的自同构倒形表示，如果存在根数为正的二次扭转，则存在中心$L$值为非零的二次扭转。

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Automorphic descent for symplectic groups: The branching problems and L-functions

abstract:We study certain automorphic descent constructions for symplectic groups, and obtain results related to branching problems of automorphic representations. As a byproduct of the construction, based on the knowledge of the global Vogan packets for ${\rm Mp}_2(\Bbb{A})$, we give a new approach to prove the result that for an automorphic cuspidal representation of ${\rm GL}_2(\Bbb{A})$ of symplectic type, if there exists a quadratic twist with positive root number, then there exist quadratic twists with non-zero central $L$-values.

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来源期刊

American Journal of Mathematics 数学-数学

CiteScore

3.20

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.