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 inGeometric and functional analysis Vol. 18; no. 5; pp. 1660 - 1695
Main Author Li, Xiaoqing
Format Journal Article
LanguageEnglish
Published Basel SP Birkhäuser Verlag Basel 01.02.2009
Subjects
Analysis
Mathematics
Mathematics and Statistics
The Rankin-Selberg L-functions
the Kuznetsov formula on GL
the Voronoi formula on GL
11-xx
subconvexity
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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