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

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

2011-03-30

arxiv.org/abs/1103.5937v2

Mathematics

Number Theory

19 pages

Scientific paper

Fix $g$ a Hecke-Maass form for $SL_3(\mathbb{Z})$. 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.

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