Quantitative non-vanishing of central values of certain L-functions on GL(2) x GL(3)

被引：0

作者：

Sugiyama, Shingo ^{[1
]}

Tsuzuki, Masao ^{[2
]}

机构：

[1] Nihon Univ, Coll Sci & Technol, Dept Math, Chiyoda Ku, 1-8-14 Suruga Dai, Tokyo 1018308, Japan

[2] Sophia Univ, Dept Sci & Technol, Chiyoda Ku, Kioi Cho 7-1, Tokyo 1028554, Japan

来源：

MATHEMATISCHE ZEITSCHRIFT | 2022年 / 301卷 / 02期

关键词：

Trace formulas; Central L-values; Non-vanishing; AUTOMORPHIC L-FUNCTIONS; TRACE FORMULA; EQUIDISTRIBUTION;

D O I：

10.1007/s00209-021-02886-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let phi be an even Hecke-Maass cusp form on SL2(Z) whose L-function does not vanish at the center of the functional equation. In this article, we obtain an exact formula of the average of triple products of phi, f and (f) over bar, where f runs over an orthonornial basis H-k of Hecke eigen elliptic cusp forms on SL2(Z) of a fixed weight k >= 4. As an application, we prove a quantitative non-vanishing results on the central values for the family of degree 6 L-functions L(s, phi x Ad f) with f in the union of H-k (K <= k < 2K) as K -> infinity.

引用

页码：1447 / 1479

页数：33

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