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doi–naganuma lift

Proceedings of the London Mathematical Society (1)

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Liftings and mean value theorems for automorphic L-functions
Kohji Matsumoto
Journal:

Proceedings of the London Mathematical Society / Volume 90 / Issue 2 / March 2005

Published online by Cambridge University Press:

25 February 2005, pp. 297-320

Print publication:

March 2005
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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.