Proceedings of the Japan Academy, Series A, Mathematical Sciences

A note on the mean value of the zeta and $L$-functions. XII

Yoichi Motohashi

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Abstract

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.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 78, Number 3 (2002), 36-41.

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148392748

Digital Object Identifier
doi:10.3792/pjaa.78.36

Mathematical Reviews number (MathSciNet)
MR1894899

Zentralblatt MATH identifier
1106.11305

Subjects
Primary: 11M06: $\zeta (s)$ and $L(s, \chi)$
Secondary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields

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

Citation

Motohashi, Yoichi. A note on the mean value of the zeta and $L$-functions. XII. Proc. Japan Acad. Ser. A Math. Sci. 78 (2002), no. 3, 36--41. doi:10.3792/pjaa.78.36. https://projecteuclid.org/euclid.pja/1148392748


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References

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