The central value of the Rankin-Selberg L-functions

Xiaoqing Li

doi:10.1007/s00039-008-0692-5

The central value of the Rankin-Selberg L-functions

Xiaoqing Li

Mathematics

Research output: Contribution to journal › Article › peer-review

59 Scopus citations

Abstract

Let f be a Maass form for SL(3, ℤ) which is fixed and u_j be an orthonormal basis of even Maass forms for SL(2, 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.

Original language	English
Pages (from-to)	1660-1695
Number of pages	36
Journal	Geometric and Functional Analysis
Volume	18
Issue number	5
DOIs	https://doi.org/10.1007/s00039-008-0692-5
State	Published - Feb 2009

Keywords

Subconvexity
The Kuznetsov formula on GL(2)
The rankin-selberg l-functions
The Voronoi formula on GL(3)

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

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KW - The Kuznetsov formula on GL(2)

KW - The rankin-selberg l-functions

KW - The Voronoi formula on GL(3)

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ER -

The central value of the Rankin-Selberg L-functions

Abstract

Keywords

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