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Fourier coefficients of $\mathrm{Sp}(4)$ Eisenstein series

Volume 213 / 2024

Siu Hang Man 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.

Authors

  • Siu Hang ManCharles University
    Faculty of Mathematics and Physics
    Department of Algebra
    186 75 Praha 8, Czechia
    e-mail

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