On the rationality of a paramodular Siegel Eisenstein series

TL;DR

This paper investigates the algebraic nature of Fourier coefficients of a specific paramodular Siegel Eisenstein series, establishing that these coefficients are contained within a number field, thus revealing their rationality properties.

Contribution

It proves that the Fourier coefficients of a certain paramodular Siegel Eisenstein series of level N^2 are algebraic and lie in a number field, advancing understanding of their rationality.

Findings

Fourier coefficients are algebraic numbers.

Coefficients lie within a specific number field.

Results apply to Eisenstein series of level N^2.

Abstract

We consider the rationality of the Fourier coefficients of a particular paramodular Siegel Eisenstein series of level $N^2$ with weight $k\geq 4$. We show that the coefficients lie in a number field.