带有尖形式Fourier系数的Gauss圆内格点问题

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

数学季刊 ›› 2025, Vol. 40 ›› Issue (3): 313-323.doi: 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

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

收稿日期:2025-02-13 出版日期:2025-09-30 发布日期:2025-09-30
作者简介:CHEN Feng (1999-), male, native of Nanxiong, Guangdong, master student of Henan University, engages in number theory
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).

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

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

Received:2025-02-13 Online:2025-09-30 Published:2025-09-30
About author:CHEN Feng (1999-), male, native of Nanxiong, Guangdong, master student of Henan University, engages in number theory
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).

摘要/Abstract

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

Abstract: 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.,...

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

中图分类号:

O156

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.

CHEN Feng. The Gauss Circle Problem Related to the Fourier Coefficients of Cusp Forms[J]. Chinese Quarterly Journal of Mathematics, 2025, 40(3): 313-323.

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带有尖形式Fourier系数的Gauss圆内格点问题

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

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