A ring of symmetric Hermitian modular forms of degree 2 with integral Fourier coefficients

2019/03/28 by Toshiyuki Kikuta, Kikuta, Toshiyuki
Mathematics · #11F30 #11F55 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1903.12036

openalex publication_date 2019/03/28 · openalex created_date 2019/04/01 · openalex updated_date 2026/07/28

Abstract

We determine the structure over ℤ of the ring of symmetric Hermitian modular forms with respect to ℚ(√(-1)) of degree 2 (with a character), whose Fourier coefficients are integers. Namely, we give a set of generators consisting of 24 modular forms. As an application of our structure theorem, we give the Sturm bounds of such the modular forms of weight k with 4| k, in the case p=2, 3. We remark that the bounds for p≥ 5 are already known.

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