Maass relations for generalized Cohen-Eisenstein series of degree two and of degree three

TL;DR

This paper extends the Maass relations to generalized Cohen-Eisenstein series of degrees two and three, which are special Siegel modular forms of half-integral weight, by establishing relations among their Fourier-Jacobi coefficients.

Contribution

It introduces generalized Maass relations for Cohen-Eisenstein series of degrees two and three, expanding understanding of their Fourier-Jacobi coefficient relations.

Findings

Established Maass relations for degree two and three Cohen-Eisenstein series.

Connected Fourier-Jacobi coefficients through new relations.

Enhanced the theory of Siegel modular forms of half-integral weight.

Abstract

The aim of this paper is to generalize the Maass relation for generalized Cohen-Eisenstein series of degree two and of degree three. Here the generalized Cohen-Eisenstein series are certain Siegel modular forms of half-integral weight, and generalized Maass relations are certain relations among Fourier-Jacobi coefficients of them.