On the Petersson norm of the Hilbert-Siegel cusp form under the Ikeda lift

In this paper, we show an arithmeticity of the ratio of the Petersson norm of the Hilbert-Siegel cusp form determined by the Ikeda lift from a Hilbert cusp form to that of the Hilbert cusp form. This is a generalization of the algebraicity of the ratio of the Petersson norm of the Siegel cusp form under the Ikeda lift of an elliptic cusp form to that of the elliptic cusp form due to Y. Choie and W. Kohnen.