In the present and the next notes of this series, we shall
try to illuminate a geometric structure behind the interactions
that have recently been observed between mean values of zeta-functions
and automorphic representations. Our discussion is hoped to
be a precursor of a unified theory of mean values of automorphic
$L$-functions that we are going to forge. In this note we shall
deal with the spectral structure over the modular group. In
the next note the Picard group will be treated, as a typical
case in the complex situation. We stress that we have been
inspired by the work [2] due to Cogdell and Pyatetskii-Shapiro.
Publié le : 2002-03-14
Classification:
Mean values of zeta-functions,
local functional equations of Jacquet-Langlands,
Gamma functions of representations,
Bessel functions of representations,
11M06,
11F70
@article{1148392748,
author = {Motohashi, Yoichi},
title = {A note on the mean value of the zeta and $L$-functions. XII},
journal = {Proc. Japan Acad. Ser. A Math. Sci.},
volume = {78},
number = {10},
year = {2002},
pages = { 36-41},
language = {en},
url = {http://dml.mathdoc.fr/item/1148392748}
}
Motohashi, Yoichi. A note on the mean value of the zeta and $L$-functions. XII. Proc. Japan Acad. Ser. A Math. Sci., Tome 78 (2002) no. 10, pp. 36-41. http://gdmltest.u-ga.fr/item/1148392748/