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

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

Yoichi Motohashi

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

Abstract

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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Primary Subjects: 11F70

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

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.pja/1188405574
Mathematical Reviews number (MathSciNet): MR2355501
Digital Object Identifier: doi:10.3792/pjaa.83.73
Zentralblatt MATH identifier: 05310169

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