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On the period of the Ikeda lift for U(m,m)

By Hidenori Katsurada

Abstract

Let K be an imaginary quadratic field, and x the Dirichlet character corresponding to the extension K/Q. Let m=2n or 2n+1 with n a positive integer. Let f be a primitive form of weight 2k+1 and and nebentype x, or a primitive form of weight 2k for SL(2,Z) according as m=2n, or m=2n+1. For such an f let I_m(f) be the lift of f to the space of modular forms of weight 2k+2n for the Hermitian modular group of degree m constructed by Ikeda. We then express the period <I_m(f), I_m(f) > of I_m(f) in terms of special values of the adjoint L-functions of f. This poves the conjecture concerning the period of the Ikeda lift proposed by Ikeda.Comment: The version arXiv:1102.4393v2. is a shortened version of the paper arXiv:1102.4393v1. Some results in arXiv:1102.4393v1 is proved in arXiv:1403.2175v2. This is a revised version of arXiv:1102.4393v

Topics: Mathematics - Number Theory, 11F55
Year: 2016
OAI identifier: oai:arXiv.org:1102.4393
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