open access

https://doi.org/10.14943/84121

https://hdl.handle.net/2115/69781

ON THE PERIOD OF THE IKEDA LIFT FOR U(m,m)

英語

2011-02-02

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

974

1-55

Let K = Q( p ¡D) be an imaginary quadratic field with discriminant ¡D, and χ 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 character χ for Γ0(D), or a primitive form of weight 2k for SL2(Z) according as m = 2n, or m = 2n+1. For such an f let Im(f) be the lift of f to the space of modular forms of weight 2k+2n and character det−k−n for the Hermitian modular group Γ(m) K constructed by Ikeda. We then express the period hIm(f), Im(f)i of Im(f) in terms of special values of the adjoint L-functions of f twisted by the character χ. This poves the conjecture concerning the period of the Ikeda lift proposed by Ikeda.

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