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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| Published in | Geometric and functional analysis Vol. 18; no. 5; pp. 1660 - 1695 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Basel
SP Birkhäuser Verlag Basel
01.02.2009
|
| Subjects | |
| Online Access | Get full text |
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| Abstract | .
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. |
|---|---|
| AbstractList | .
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. |
| Author | Li, Xiaoqing |
| Author_xml | – sequence: 1 givenname: Xiaoqing surname: Li fullname: Li, Xiaoqing email: X129@math.buffalo.edu organization: Department of Mathematics, College of Arts and Sciences, University at Buffalo, The State University of New York |
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| Keywords | The Rankin-Selberg L-functions the Kuznetsov formula on GL the Voronoi formula on GL 11-xx subconvexity |
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| Snippet | .
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... |
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| StartPage | 1660 |
| SubjectTerms | Analysis Mathematics Mathematics and Statistics |
| Title | The Central value of the Rankin–Selberg L-Functions |
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