On a shifted convolution sum problem

被引：3

作者：

Munshi, Ritabrata ^{[1
]}

机构：

[1] Indian Stat Inst, Theoret Stat & Math Unit, 203 BT Rd, Kolkata 700108, India

来源：

JOURNAL OF NUMBER THEORY | 2022年 / 230卷

关键词：

GL(2) forms; Shifted convolution sum; CIRCLE METHOD; BOUNDS;

D O I：

10.1016/j.jnt.2020.12.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let f be a holomorphic newform of prime level p and trivial nebentypus. For p(1+epsilon) << M << p(3-epsilon), and 0 < vertical bar u vertical bar << M/p we prove that Sigma(infinity)(m=1) lambda(f)(m)lambda(f) (m +pu)F(m/M) << p(1/4+epsilon) M-3/4 where F is a compactly supported smooth bump function. (C) 2021 Elsevier Inc. All rights reserved.

引用

页码：225 / 232

页数：8

共 7 条

[1] A burgess-like subconvex bound for twisted L-functions
Blomer, V.
Harcos, G.
Michel, P.
Mao, Z.
[J]. FORUM MATHEMATICUM, 2007, 19 (01) : 61 - 105
[2] BOUNDS FOR AUTOMORPHIC L-FUNCTIONS
DUKE, W
FRIEDLANDER, J
IWANIEC, H
[J]. INVENTIONES MATHEMATICAE, 1993, 112 (01) : 1 - 8
[3] HeathBrown DR, 1996, J REINE ANGEW MATH, V481, P149
[4] Rankin-Selberg L-functions in the level aspect
Kowalski, E
Michel, P
Vanderkam, J
[J]. DUKE MATHEMATICAL JOURNAL, 2002, 114 (01) : 123 - 191
[5] Michel P., 2007, Automorphic Forms and Applications, V12, P179
[6] THE CIRCLE METHOD AND BOUNDS FOR L-FUNCTIONS III: t-ASPECT SUBCONVEXITY FOR GL(3) L-FUNCTIONS
Munshi, Ritabrata
[J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 28 (04) : 913 - 938
[7] THE CIRCLE METHOD AND BOUNDS FOR L-FUNCTIONS, II: SUB CONVEXITY FOR TWISTS OF GL(3) L-FUNCTIONS
Munshi, Ritabrata
[J]. AMERICAN JOURNAL OF MATHEMATICS, 2015, 137 (03) : 791 - 812

← 1 →