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

CHEN Feng

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

Chinese Quarterly Journal of Mathematics >

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

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

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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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

Cite this article

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

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