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.

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