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March 2002 A note on the mean value of the zeta and $L$-functions. XII
Yoichi Motohashi
Proc. Japan Acad. Ser. A Math. Sci. 78(3): 36-41 (March 2002). DOI: 10.3792/pjaa.78.36


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.


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Yoichi Motohashi. "A note on the mean value of the zeta and $L$-functions. XII." Proc. Japan Acad. Ser. A Math. Sci. 78 (3) 36 - 41, March 2002.


Published: March 2002
First available in Project Euclid: 23 May 2006

zbMATH: 1106.11305
MathSciNet: MR1894899
Digital Object Identifier: 10.3792/pjaa.78.36

Primary: 11M06
Secondary: 11F70

Keywords: Bessel functions of representations , Gamma functions of representations , local functional equations of Jacquet-Langlands , Mean values of zeta-functions

Rights: Copyright © 2002 The Japan Academy

Vol.78 • No. 3 • March 2002
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