Spectral moment formulae for GL(3) × GL(2) L-functions I : The cuspidal case

IF 0.9 1区数学 Q2 MATHEMATICS

Algebra & Number Theory Pub Date : 2024-10-07 DOI:10.2140/ant.2024.18.1817

Chung-Hang Kwan

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引用次数: 0

Abstract

Spectral moment formulae of various shapes have proven very successful in studying the statistics of central $L$ -values. We establish, in a completely explicit fashion, such formulae for the family of $GL (3) \times GL (2)$ Rankin–Selberg $L$ -functions using the period integral method. Our argument does not rely on either the Kuznetsov or Voronoi formulae. We also prove the essential analytic properties and derive explicit formulae for the integral transform of our moment formulae. We hope that our method will provide deeper insights into moments of $L$ -functions for higher-rank groups.

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GL(3) × GL(2) L 函数的谱矩公式 I : 偶态情况

事实证明，各种形状的谱矩公式在研究中心 L 值的统计方面非常成功。我们采用周期积分法，以完全明确的方式为 GL (3)× GL (2) 兰金-塞尔伯格 L 函数族建立了这样的公式。我们的论证既不依赖库兹涅佐夫公式，也不依赖沃罗诺伊公式。我们还证明了基本的解析性质，并推导出矩公式积分变换的明确公式。我们希望我们的方法能为高阶群的 L 函数矩提供更深入的见解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebra & Number Theory MATHEMATICS-

CiteScore

1.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： ANT’s inclusive definition of algebra and number theory allows it to print research covering a wide range of subtopics, including algebraic and arithmetic geometry. ANT publishes high-quality articles of interest to a broad readership, at a level surpassing all but the top four or five mathematics journals. It exists in both print and electronic forms. The policies of ANT are set by the editorial board — a group of working mathematicians — rather than by a profit-oriented company, so they will remain friendly to mathematicians'' interests. In particular, they will promote broad dissemination, easy electronic access, and permissive use of content to the greatest extent compatible with survival of the journal. All electronic content becomes free and open access 5 years after publication.