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

Abstract

In 2000, Hafner and Stopple proved a conjecture of Zagier which states that the constant term of the automorphic function |∆(x+iy)|2 i.e., the Lambert series Σ∞n=1 τ (n)2e−4πny can be expressed in terms of the non-trivial zeros of the Riemann zeta function. In this article, we study an asymptotic expansion of a generalized version of the aforementioned Lambert series associated to Siegel cusp forms. 2010 Mathematics Subject Classification. Primary 11M06, 11M26; Secondary 11N37.