Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 72, No. 4, pp. 1047-1054, 2022

A quadratic form with prime variables associated with Hecke eigenvalues of a cusp form

Guodong Hua

Received September 10, 2021. Published online June 17, 2022.

Abstract: Let $f$ be a normalized primitive holomorphic cusp form of even integral weight $k$ for the full modular group ${\rm SL}(2,\mathbb{Z})$, and denote its $n$th Fourier coefficient by $\lambda_f(n)$. We consider the hybrid problem of quadratic forms with prime variables and Hecke eigenvalues of normalized primitive holomorphic cusp forms, which generalizes the result of D. Y. Zhang, Y. N. Wang (2017).

Keywords: circle method; cusp form; Fourier coefficient

Classification MSC: 11F30, 11F41, 11N37

DOI: 10.21136/CMJ.2022.0329-21

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Guodong Hua, School of Mathematics and Statistics, Weinan Normal University, Chaoyang Street, Shaanxi, Weinan 714099, P. R. China, e-mail: gdhua@mail.sdu.edu.cn

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