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

Xiaoqing Li

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

Number Theory 2008-12-02 v1

Authors: Xiaoqing Li

Abstract

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 $1/2.$

Keywords

Rankin-Selberg L-function Maass form central value asymptotic formula simultaneous nonvanishing

Cite

@article{arxiv.0812.0035,
  title  = {The central value of the Rankin-Selberg $L$-functions},
  author = {Xiaoqing Li},
  journal= {arXiv preprint arXiv:0812.0035},
  year   = {2008}
}

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