The central value of the Rankin-Selberg $L$-functions

Details The central value of the Rankin-Selberg $L$-functions The central value of the Rankin-Selberg $L$-functions

2008-11-29

arxiv.org/abs/0812.0035v1

Mathematics

Number Theory

Scientific paper

Let $f$ be a Maass form for $SL(3, \mathbb{Z})$ which is fixed and $u_j$ be an orthonormal basis of even Maass forms for $SL(2, \mathbb{Z}),$ we prove an asymptotic formula for the average of the product of the Rankin-Selberg $L$-function of $f$ and $u_j$ and the $L$-function of $u_j$ at the central value 1/2. This implies simultaneous nonvanishing results of these $L$-functions at $1/2.$

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