Proceedings of the Japan Academy, Series A, Mathematical Sciences
- Proc. Japan Acad. Ser. A Math. Sci.
- Volume 78, Number 3 (2002), 36-41.
A note on the mean value of the zeta and $L$-functions. XII
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  due to Cogdell and Pyatetskii-Shapiro.
Proc. Japan Acad. Ser. A Math. Sci., Volume 78, Number 3 (2002), 36-41.
First available in Project Euclid: 23 May 2006
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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