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

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

2007-03-20

arxiv.org/abs/math/0703571v2

Mathematics

Number Theory

6 pages in a double-column format

Scientific paper

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. In this new version we added details to all aspects of our argument especially for the treatment of the discrete series and the continuous spectrum.

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