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Liftings and mean value theorems for automorphic L-functions

Published online by Cambridge University Press:  25 February 2005

Kohji Matsumoto
Kohji Matsumoto
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464–8602, Japan. E-mail: kohjimat@math.nagoya-u.ac.jp
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Abstract

A general mean value theorem for Dirichlet series, with a sharp error estimate near the boundary of the critical strip, is proved. Applications of this theorem to various automorphic $L$-functions are discussed. Moreover, sharp upper bounds of mean square values of $L$-functions are obtained when they are attached to lifted forms, such as Doi–Naganuma and Ikeda lifts in the theory of Siegel modular forms.

Keywords

mean valueautomorphic L-functionRankin–Selberg L functionDoi–Naganuma liftIkeda lift11F6611M41
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 90 , Issue 2 , March 2005 , pp. 297 - 320
Copyright
2005 London Mathematical Society

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