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Ikeda's conjecture on the period of the Duke-Imamoglu-Ikeda lift
en
KATSURADA Hidenori
KAWAMURA Hisa-aki
Let k and n be positive even integers. For a cuspidal Hecke eigenform h in the Kohnen plus space of weight k - n/2 + 1/2 for Γ0(4), let In(h) be the Duke-Imamoglu-Ikeda lift of h in the space of cusp forms of weight k for Spn(Z), and f the primitive form of weight 2k - n for SL2(Z) corresponding to h under the Shimura correspondence. We then express the ratio <In(h), In(h)>/<h, h> of the period of In(h) to that of h in terms of special values of certain L-functions of f. This proves the conjecture proposed by Ikeda concerning the period of the Duke-Imamoglu-Ikeda lift.
Proceedings of the London Mathematical Society. Ser. 3
111
5
445-483
2015
London Mathematical Society
info:doi/10.1112/plms/pdv011
413
00246115
AA0078577X
© London Mathematical Society
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