Geodesic
A quadratic form with prime variables associated with Hecke eigenvalues of a cusp form
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 4, pp. 1047-1054
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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).
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).
DOI : 10.21136/CMJ.2022.0329-21
Classification : 11F30, 11F41, 11N37
Keywords: circle method; cusp form; Fourier coefficient 
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Hua, Guodong. A quadratic form with prime variables associated with Hecke eigenvalues of a cusp form. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 4, pp. 1047-1054. doi: 10.21136/CMJ.2022.0329-21

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