具有递归关系的阿基米德Rankin-Selberg积分的演算

IF 0.7 3区数学 Q2 MATHEMATICS

Representation Theory Pub Date : 2022-07-06 DOI:10.1090/ert/618

Taku Ishii, Tadashi Miyazaki

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引用次数: 0

摘要

摘要:设$n$和$n ' $为正整数，使得$n-n ' \in \{0,1\}$。设$F$为$\mathbb {R}$或$\mathbb {C}$。设$K_n$和$K_{n '}$分别是$\ mathm {GL}(n,F)$和$\ mathm {GL}(n '，F)$的最大紧子群。利用递归关系，给出了$\ mathm {GL}(n,F)$和$\ mathm {GL}(n '，F)$的主级数表示对在最小$K_n$-和$K_{n '}$-类型上的阿基米德兰金-塞尔伯格积分的显式描述。我们关于$F=\mathbb {C}$的结果可以应用于自同构$L$-函数的临界值的算术研究。

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Calculus of archimedean Rankin–Selberg integrals with recurrence relations

Abstract:Let $n$ and $n’$ be positive integers such that $n-n’\in \{0,1\}$. Let $F$ be either $\mathbb {R}$ or $\mathbb {C}$. Let $K_n$ and $K_{n’}$ be maximal compact subgroups of $\mathrm {GL}(n,F)$ and $\mathrm {GL}(n’,F)$, respectively. We give the explicit descriptions of archimedean Rankin–Selberg integrals at the minimal $K_n$- and $K_{n’}$-types for pairs of principal series representations of $\mathrm {GL}(n,F)$ and $\mathrm {GL}(n’,F)$, using their recurrence relations. Our results for $F=\mathbb {C}$ can be applied to the arithmetic study of critical values of automorphic $L$-functions.

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来源期刊

Representation Theory MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. Representation Theory is an open access journal freely available to all readers and with no publishing fees for authors.