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

Abstract

In 2000, Hafner and Stopple proved a conjecture of Zagier which states that the constant term of the automorphic function |Δ(x+iy)|2, i.e., the Lambert series ∑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 with Siegel cusp forms. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.