Absolute values of L-functions for GL(n, R) at the point 1

被引：6

作者：

Lau, Yuk-Kam ^{[1
]}

Wang, Yingnan ^{[2
]}

机构：

[1] Univ Hong Kong, Dept Math, Pokfulam Rd, Hong Kong, Hong Kong, Peoples R China

[2] Shenzhen Univ, Coll Math & Stat, Shenzhen 518060, Guangdong, Peoples R China

来源：

ADVANCES IN MATHEMATICS | 2018年 / 335卷

基金：

中国国家自然科学基金;

关键词：

Automorphic forms on GL(n); L-functions; Extreme values at 1; Complex moments; AUTOMORPHIC L-FUNCTIONS; POWER L-FUNCTIONS; DENSITY-THEOREM; EXTREME VALUES; EDGE; MOMENTS;

D O I：

10.1016/j.aim.2018.07.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the values of vertical bar L(1,F)vertical bar for Hecke-Maass cusp forms F on SL(n,Z) (n >= 3) of large Langlands parameters. New unconditional results on the extreme values and conditional results on the size range are derived, which determine precisely the order of magnitude of L(1, F). In addition, we enhance the new average estimate toward the Ramanujan Conjecture due to Matz and Templier. An application of the Hecke multiplicativity to the Littlewood-Richardson rule for a product of two Schur polynomials is cultivated. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：759 / 808

页数：50

共 37 条

[1]

Agashe A., GEN KRONECKERS 1 LIM

[2]

[Anonymous], 1941, Progress in Mathematics

[3]

Bump D, 2013, GRAD TEXTS MATH, V225, P1, DOI 10.1007/978-1-4614-8024-2

[4]

Chowla S., 1949, Proc. Lond. Math. Soc, V50, P423

[5]

Cogdell J, 2004, INT MATH RES NOTICES, V2004, P1561

[6] Eigenvalues, invariant factors, highest weights, and Schubert calculus [J].

Fulton, W .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 37 (03) :209-249

[7]

Fulton W., 1991, REPRESENTATION THEOR

[8]

Goldfeld D., STANDARD ZERO FREE R

[9]

Goldfeld D., 2006, AUTOMORPHIC FORMS L

[10] The distribution of values of L(1, χd) [J].

Granville, A ;

Soundararajan, K .

GEOMETRIC AND FUNCTIONAL ANALYSIS, 2003, 13 (05) :992-1028

← 1 2 3 4 →