Fourier coefficients of $\mathrm{Sp}(4)$ Eisenstein series
Volume 213 / 2024
Acta Arithmetica 213 (2024), 227-271
MSC: Primary 11E45; Secondary 11F12, 11F30, 11F46
DOI: 10.4064/aa230511-16-1
Published online: 24 April 2024
Abstract
We compute explicit formulae for the constant terms and Fourier coefficients for Eisenstein series on Sp$(4,\mathbb R)$, in terms of zeta functions and Whittaker functions. We also develop a generalisation of Ramanujan sums to Sp$(4,\mathbb Z)$, which appear as coefficients in the Fourier expansion for the minimal Eisenstein series.
