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Research Article | Open Access

High power sums of Fourier coefficients of holomorphic cusp forms and their applications

Guangwei Hu, Huixue Lao( ), Huimin Pan
School of Mathematics and Statistics, Shandong Normal University, Ji'nan 250358, China
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Abstract

Let λf(n) be the nth normalized Fourier coefficient of a holomorphic cusp form f for the full modular group. In this paper, we established asymptotic formulae for high power sums of Fourier coefficients of cusp forms and further improved previous results. Moreover, as an application, we studied the signs of the sequences {λf(n)} and {λf(n)λg(n)} in short intervals, and presented some quantitative results for the number of sign changes for n≤x.

Keywords

cusp formL-functionFourier coefficientsign change
CLC number: 11F30, 11F66, 11N37

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AIMS Mathematics
Volume 9 Issue 9,
September 2024
Pages 25166-25183
DOI: 10.3934/math.20241227

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Cite this article:
Hu G, Lao H, Pan H. High power sums of Fourier coefficients of holomorphic cusp forms and their applications. AIMS Mathematics, 2024, 9(9): 25166-25183. https://doi.org/10.3934/math.20241227

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Received: 30 June 2024
Revised: 19 August 2024
Accepted: 21 August 2024
Published: 15 September 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)