A twist of the Gauss circle problem by holomorphic cusp forms

被引：3

作者：

Acharya, Ratnadeep ^{[1
]}

机构：

[1] RKMVERI, Belur Math 711202, Howrah, India

来源：

RESEARCH IN NUMBER THEORY | 2022年 / 8卷 / 01期

关键词：

D O I：

10.1007/s40993-021-00299-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let f be a holomorphic cusp form of even weight k for the group Gamma(0)(4N) with N is an element of N. We prove that S-f(X) := Sigma(k,l is an element of Z)Sigma(k2+l2 <= X)lambda(f)(k(2) + l(2)) <<(k,N,epsilon) X1/2+epsilon for any epsilon > 0, where lambda(f)(n) denotes the normalized n-th Fourier coefficients of f.

引用

页数：14

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