Simultaneous non-vanishing of $GL(3)\times GL(2)$ and GL(2) $L$-functions

Abstract

Fix $g$ a Hecke-Maass form for $S{L}_3(\mathbb{Z})$. Let $q$ be any large prime number. In the family of holomorphic newforms $f$ of level $q$ and fixed weight, 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.

19 pages

References in corpus (1)

• The second moment of $GL(3)\times GL(2)$ $L$-functions, integrated

Cited by in corpus (4)

• The second moment of twisted modular L-functions
• Twisted moments of L-functions and spectral reciprocity
• The Voronoi formula and double Dirichlet series
• Spectral reciprocity via integral representations