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Liftings and Mean Value Theorems for Automorphic L ‐Functions
Author(s) -
Matsumoto Kohji
Publication year - 2005
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611504015096
Subject(s) - mathematics , automorphic form , mean value , dirichlet distribution , dirichlet series , automorphic l function , pure mathematics , mean value theorem (divided differences) , mean square , converse theorem , value (mathematics) , mathematical analysis , boundary value problem , statistics , picard–lindelöf theorem , fixed point theorem
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. 2000 Mathematics Subject Classification 11F66, 11M41.