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On general divisor problems of Hecke eigenvalues of cusp forms

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Abstract

Let f be a primitive holomorphic cusp form of even integral weight k for the full modular group \(\Gamma =SL(2,{\mathbb {Z}})\). Let \(\lambda _{f}(n)\) denote the nth normalized Fourier coefficient of f. In this paper, we consider the general divisor problem of higher moments of \(\lambda _{f}(n)\), and also consider the same problem over sums of two squares.

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Acknowledgements

This work was financially supported in part by The National Key Research and Development Program of China (Grant No. 2021YFA1000700), Natural Science Basic Research Program of Shaanxi (Program Nos. 2023-JC-QN-0024, 2023-JC-YB-077), Foundation of Shaanxi Educational Committee (2023-JC-YB-013) and Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No. 22JSQ010).

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  1. School of Mathematics and Statistics, Weinan Normal University, Shaanxi, Weinan, 714099, China

    Guodong Hua

  2. School of Mathematics, Shandong University, Shandong, Jinan, 250100, China

    Guodong Hua

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  1. Guodong Hua
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Hua, G. On general divisor problems of Hecke eigenvalues of cusp forms. Period Math Hung 87, 340–350 (2023). https://doi.org/10.1007/s10998-023-00523-8

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