带有尖形式Fourier系数的Gauss圆内格点问题

陈锋

doi:10.13371/j.cnki.chin.q.j.m.2025.03.007

数学季刊 >

2025 , Vol. 40 >Issue 3: 313 - 323

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2025.03.007

带有尖形式Fourier系数的Gauss圆内格点问题

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School of Mathematics and Statistics, Henan University, Kaifeng 475004, China

CHEN Feng (1999-), male, native of Nanxiong, Guangdong, master student of Henan University, engages in number theory

收稿日期: 2025-02-13

网络出版日期: 2025-09-30

基金资助

Supported in part by the Natural Science Foundation of Henan Youth Foundation (Grant No. 222300420034) and National Natural Science Foundation of China (Grant No. 11871193).

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The Gauss Circle Problem Related to the Fourier Coefficients of Cusp Forms

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School of Mathematics and Statistics, Henan University, Kaifeng 475004, China

CHEN Feng (1999-), male, native of Nanxiong, Guangdong, master student of Henan University, engages in number theory

Received date: 2025-02-13

Online published: 2025-09-30

Supported by

Supported in part by the Natural Science Foundation of Henan Youth Foundation (Grant No. 222300420034) and National Natural Science Foundation of China (Grant No. 11871193).

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摘要

Let f be a Hecke eigenform of even integral weight k for the full modular group SL₂(Z). Denote by λ_f (n) the nth normalized coefficient of f. The sum of Fourier coefficients of cusp form over the quadratic polynomial m² +n² is considered, i.e.,...

关键词： Cusp form; Quadratic form; L-function

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陈锋 . 带有尖形式Fourier系数的Gauss圆内格点问题[J]. 数学季刊, 2025 , 40(3) : 313 -323 . DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.007

Abstract

Key words： Cusp form; Quadratic form; L-function

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