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June 2007 A note on the mean value of the zeta and $L$-functions. XV
Yoichi Motohashi
Proc. Japan Acad. Ser. A Math. Sci. 83(6): 73-78 (June 2007). DOI: 10.3792/pjaa.83.73


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.


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Yoichi Motohashi. "A note on the mean value of the zeta and $L$-functions. XV." Proc. Japan Acad. Ser. A Math. Sci. 83 (6) 73 - 78, June 2007.


Published: June 2007
First available in Project Euclid: 29 August 2007

zbMATH: 1196.11073
MathSciNet: MR2355501
Digital Object Identifier: 10.3792/pjaa.83.73

Primary: 11F70

Keywords: Automorphic representations , Kirillov model , Mean values of automorphic $L$-functions

Rights: Copyright © 2007 The Japan Academy

Vol.83 • No. 6 • June 2007
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