On the Divisibility Properties of the Fourier Coefficients of Meromorphic Hilbert Modular Forms

Baptiste Depouilly

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arXiv · 2411.00701

On the Divisibility Properties of the Fourier Coefficients of Meromorphic Hilbert Modular Forms

Baptiste Depouilly

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Abstract

Following Zagier, this work studies the rationality and divisibility of Fourier coefficients of meromorphic Hilbert modular forms associated with real quadratic fields, using theta lifts and weak Maass forms. We establish conditions where these coefficients are rational with bounded denominators and demonstrate divisibility properties under suitable linear combinations.

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Baptiste Depouilly. 2024-11-01. On the Divisibility Properties of the Fourier Coefficients of Meromorphic Hilbert Modular Forms. https://arxiv.org/abs/2411.00701

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