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

被引：1

作者：

Kwan, Chung-Hang ^{[1
]}

机构：

[1] UCL, Dept Math, London, England

来源：

ALGEBRA & NUMBER THEORY | 2024年 / 18卷 / 10期

基金：

英国工程与自然科学研究理事会;

关键词：

automorphic forms; automorphic L-functions; Maass forms; moments of L-functions; Rankin-Selberg L-functions; period integrals; Whittaker functions; hypergeometric functions; Poincare series; SELBERG L-FUNCTIONS; TWISTED L-FUNCTIONS; SUBCONVEXITY PROBLEM; AUTOMORPHIC-FORMS; SERIES; WEYL; TRANSFORMS; KUZNETSOV; WEIGHT; BOUNDS;

D O I：

10.2140/ant.2024.18.1817

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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) ( 3 ) x GL(2) ( 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.

引用

页码：1817 / 1862

页数：49

共 63 条

[1] Mixed moment of GL(2) and GL(3) L-functions [J].