Proceedings of the Japan Academy, Series A, Mathematical Sciences

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

Yoichi Motohashi

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The aim of the present article is to render the spectral theory of mean values of automorphic $L$-functions -- in a unified fashion. This is an outcome of the investigation commenced with the parts XII and XIV, where a framework was laid on the basis of the theory of automorphic representations and a general approach to the mean values was envisaged. We restrict ourselves to the situation offered by the full modular group, solely for the sake of simplicity. Details and extensions are to be published elsewhere.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 83, Number 6 (2007), 73-78.

First available in Project Euclid: 29 August 2007

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Zentralblatt MATH identifier

Primary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields

Mean values of automorphic $L$-functions automorphic representations Kirillov model


Motohashi, Yoichi. A note on the mean value of the zeta and $L$-functions. XV. Proc. Japan Acad. Ser. A Math. Sci. 83 (2007), no. 6, 73--78. doi:10.3792/pjaa.83.73.

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