Geometric and Functional Analysis

, Volume 18, Issue 5, pp 1660–1695

The Central value of the Rankin–Selberg L-Functions

Article

DOI: 10.1007/s00039-008-0692-5

Cite this article as:
Li, X. GAFA Geom. funct. anal. (2009) 18: 1660. doi:10.1007/s00039-008-0692-5

Abstract.

Let f be a Maass form for SL\((3, {\mathbb{Z}})\) which is fixed and uj 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 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.

AMS Mathematics Subject Classification:

11-xx 

Keywords and phrases:

The Rankin-Selberg L-functions subconvexity the Kuznetsov formula on GL(2) the Voronoi formula on GL(3) 

Copyright information

© Birkhaeuser 2008

Authors and Affiliations

  1. 1.Department of Mathematics, College of Arts and SciencesUniversity at Buffalo, The State University of New YorkBuffaloUSA

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