An asymptotic expansion for a Lambert series associated to Siegel cusp forms of degree n

Abstract

Utilizing inverse Mellin transform of the symmetric square L-function attached to Ramanujan tau function, Hafner and Stopple proved a conjecture of Zagier, which states that the constant term of the automorphic function y12|Δ(z)|2, i.e. the Lambert series y12∑ n=1∞τ(n)2e-4πny can be expressed in terms of the nontrivial zeros of the Riemann zeta function. This study examines certain Lambert series associated to Siegel cusp forms of degree n twisted by a character χ and observes a similar phenomenon. © 2025 World Scientific Publishing Company.