On the Fourier coefficients of Siegel Eisenstein series of degree 3 of an odd prime level with the quadratic character

Abstract

In this paper we give an explicit formula of the Fourier coefficients of the Siegel Eisenstein series of degree 3, level 𝑝 with quadratic character. For the calculation we use the result of the generalized Gauss sum computed by Hiroshi Saito. After the tedious calculation we can get a rather simple result.