Abstract
We prove the algebraicity of the ratio of the Petersson norm of a holomorphic Hilbert modular form over a totally real number field and the norm of its Saito–Kurokawa lift. We prove a similar result for the Ikeda lift of an elliptic modular form. In order to obtain these we combine some results on local symplectic groups to generalize a special value of the standard L-function attached to a Siegel–Hilbert cuspform.
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