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

2024/11/01 by Baptiste Depouilly, Depouilly, Baptiste
Mathematics · #Algebraic and Geometric Analysis #Analytic and geometric function theory #FOS: Mathematics #Holomorphic and Operator Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2411.00701

openalex publication_date 2024/11/01 · openalex created_date 2024/11/14 · openalex updated_date 2026/07/28

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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