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On power sums of Fourier coefficients of cusp forms.

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Titel: On power sums of Fourier coefficients of cusp forms.
Autoren: Liu, Huafeng1 (AUTHOR) huafengliu@sdnu.edu.cn, Lü, Jingyang1 (AUTHOR) lvjingyang@sdnu.edu.cn
Quelle: QM - Quaestiones Mathematicae. Nov2025, p1-18. 18p.
Schlagwörter: *MODULAR forms, *FOURIER analysis, *ASYMPTOTIC analysis, *MODULAR groups, *NUMBER theory
Abstract: AbstractWe denote by λf (n) the n-th normalized Fourier coefficient of primitive holomorphic cusp form of even integral weight k ≥ 2 for the full modular group SL(2,). In this paper, we prove asymptotic formulae for l-th power sums of two types related to the Fourier coefficient λf (n), which refines previous results. [ABSTRACT FROM AUTHOR]
Datenbank: Academic Search Index
Beschreibung
Abstract:AbstractWe denote by λ<italic>f</italic> (<italic>n</italic>) the <italic>n</italic>-th normalized Fourier coefficient of primitive holomorphic cusp form of even integral weight <italic>k</italic> ≥ 2 for the full modular group <italic>SL</italic>(2,). In this paper, we prove asymptotic formulae for <italic>l</italic>-th power sums of two types related to the Fourier coefficient λ<italic>f</italic> (<italic>n</italic>), which refines previous results. [ABSTRACT FROM AUTHOR]
ISSN:16073606
DOI:10.2989/16073606.2025.2576678