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September 10, 2025

New Bounds for Fundamental Fourier coefficients of Siegel modular forms

Key Points

New bounds for the Fourier coefficients were established, enhancing our understanding of modular forms.
Utilizing a method by Iwaniec, the study achieves strong estimates for fundamental Fourier coefficients.
The Fourier–Jacobi expansion of degree two Siegel modular forms underpins the results obtained.
These findings may lead to further advancements in the field of modular forms and their applications.

Abstract

Abstract We prove new bounds for the Fourier coefficients of Jacobi forms using a method of Iwaniec. In view of the Fourier–Jacobi expansion of degree two Siegel modular forms, we can use these to obtain strong bounds on fundamental Fourier coefficients of Siegel modular forms.

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Edgar Assing (Tue,) studied this question.

synapsesocial.com/papers/68c1bd4254b1d3bfb60eecb1 https://doi.org/https://doi.org/10.1093/imrn/rnaf224