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Establish refined asymptotic formulae for two types of power sums associated with the normalized Fourier coefficients of primitive holomorphic cusp forms.

November 4, 2025Quaestiones Mathematicae

On power sums of Fourier coefficients of cusp forms

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Establish refined asymptotic formulae for two types of power sums associated with the normalized Fourier coefficients of primitive holomorphic cusp forms.
Analyzed normalized Fourier coefficients of primitive holomorphic cusp forms of even integral weight under the full modular group.
Evaluated the asymptotic behavior and analytic properties across two distinct classes of power sums.
Derived new asymptotic formulae for two variants of power sums involving normalized Fourier coefficients.
Refined existing error terms and analytical approximations established in earlier literature.

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Implication

Mathematical analysis derives refined asymptotic formulae for power sums of Fourier coefficients in modular cusp forms, indicating improved precision over previous estimates.

Cite This Study

Liu et al. (2025) studied this question.

synapsesocial.com/papers/6a71c469c1a24a6142dbbf2e https://doi.org/10.2989/16073606.2025.2576678

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Implication

Mathematical analysis derives refined asymptotic formulae for power sums of Fourier coefficients in modular cusp forms, indicating improved precision over previous estimates.

On power sums of Fourier coefficients of cusp forms

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Discussion

Implication

Cite This Study

On power sums of Fourier coefficients of cusp forms

Key Points

Discussion

Implication

Cite This Study

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