Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Simultaneous non-vanishing of GL(3) × GL(2) and GL(2) L-functions


a1 Mathematisches Institut, Georg-August Universität Göttingen, Bunsenstraße 3-5, D-37073 Göttingen, Germany. e-mail:


Fix g a Hecke–Maass form for SL3(). In the family of holomorphic newforms f of fixed weight and large prime level q, we find the average value of the product $L(\half,g\times f)L(\half,f)$. From this we derive a result on the simultaneous non-vanishing of these L-functions at the central point.

(Received March 29 2011)

(Revised August 18 2011)

(Online publication December 12 2011)