The Central value of the Rankin–Selberg L-Functions

. Let f be a Maass form for SL which is fixed and u j be an orthonormal basis of even Maass forms for SL , 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 nonva...

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Bibliographic Details
Published in:Geometric and functional analysis 2009-02, Vol.18 (5), p.1660-1695
Main Author: Li, Xiaoqing
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
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Summary:. Let f be a Maass form for SL which is fixed and u j be an orthonormal basis of even Maass forms for SL , 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.
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-008-0692-5