An asymptotic expansion for a Lambert series associated to Siegel cusp forms of degree <i>n</i>

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 [Formula: see text] i.e. the Lambert series [Formula: see text] 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 [Formula: see text] and observes a similar phenomenon.