Chinese Quarterly Journal of Mathematics ›› 2025, Vol. 40 ›› Issue (3): 313-323.doi: 10.13371/j.cnki.chin.q.j.m.2025.03.007

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

  

  1. 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).

Abstract: Let f be a Hecke eigenform of even integral weight k for the full modular group SL2(Z). Denote by λf (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

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