Sum of the Fourier coefficients of SL(3, Z) Hecke Maass forms over quadratics

被引：0
|
作者：
Chanana, Himanshi [1 ]
Singh, Saurabh Kumar [1 ]
机构：
[1] Indian Inst Technol Kanpur, Dept Math & Stat, Kalyanpur 208016, India
来源：
JOURNAL OF NUMBER THEORY | 2023年 / 248卷
关键词：
Maass forms; Hecke eigenforms; Voronoi summation formula; Poisson summation formula; SUMMATION; BOUNDS;
D O I：
10.1016/j.jnt.2023.01.011
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let A(1, n) denote the (1, n)-th Fourier coefficients of a SL(3, Z) Hecke eigenform. Let Q(x, y) be a symmetric positive definite quadratic form. In this paper, we shall prove that S := Sigma(m <= X) Sigma(n <= X) A(1, Q(m,n))W-1 (m/X) W-2 (n/X) << X2-1/68+epsilon, for any positive epsilon > 0, where W-1 and W-2 are smooth bump functions supported on the interval [1, 2]. (c) 2023 Elsevier Inc. All rights reserved.
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页码：242 / 260
页数：19
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