Moments of Central $L$-values for Maass Forms over Imaginary Quadratic Fields

Abstract

In this paper, over imaginary quadratic fields, we consider the family of L-functions Lps, f q for an orthonormal basis of spherical Hecke-Maass forms f with Archimedean parameter t f . We establish asymptotic formulae for the twisted first and second moments of the central values L `1 2 , f ˘, which can be applied to prove that at least 33% of L `1 2 , f ˘with t f ď T are non-vanishing as T Ñ 8. Our main tools are the spherical Kuznetsov trace formula and the Voronoï summation formula over imaginary quadratic fields.