An asymptotic expansion for a twisted Lambert series associated to a cusp form and the Möbius function: level aspect

Abstract

Recently, Juyal, Maji and Sathyanarayana have studied a Lambert series associated with a cusp form over the full modular group and the Möbius function. In this paper, we investigate the Lambert series, where a f (n) is the nth Fourier coefficient of a cusp form f over any congruence subgroup, and ψ and ψ ′ are primitive Dirichlet characters. This extends the earlier work to the case of higher level subgroups and also gives a character analogue.