Work

Formal Siegel modular forms for arithmetic subgroups

Year: 2024

Type: article

Abstract: The notion of formal Siegel modular forms for an arithmetic subgroup Γ \Gamma of the symplectic group of genus n n is a generalization of symmetric formal Fourier-Jacobi series. Assuming an upper bound on the affine covering number of the Siegel modular variety associated with Γ \Gamma , we prove that all formal Siegel modular forms are given by Fourier-Jacobi expansions of classical holomorphic Siegel modular forms. We also show that the required upper bound is always met if 2 ≤ n ≤ 4 2\leq n \leq 4 . As an application we consider the case of the paramodular group of squarefree level and genus 2 2 .

Source: Transactions of the American Mathematical Society Series B

DOI: 10.1090/btran/216

Authors: Jan Bruinier, Martin Raum

Institutions: Technische Universität Darmstadt, Chalmers University of Technology, University of Gothenburg

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,750

Funders: Deutsche Forschungsgemeinschaft, Vetenskapsrådet