Fourier coefficients of $\operatorname{Sp}(4)$ Eisenstein Series

Abstract

We compute explicit formulae for the constant terms and Fourier coefficients for Eisenstein series on $\operatorname{Sp}(4,\mathbb{R})$, in terms of zeta functions and Whittaker functions. We also develop a generalisation of Ramanujan sums to $\operatorname{Sp}(4,\mathbb{Z})$, which appears as coefficients in the Fourier expansion for the minimal Eisenstein series.