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We prove an algebraicity property for a certain ratio of Petersson norms associated to a Siegel cusp form of degree 2 (and arbitrary level) whose adelization generates a weak endoscopic lift. As a preparation for this, we explicate various features of the correspondence between scalar valued Siegel cusp forms of degree  n  and automorphic representations onGSp    2  n${{\rm GSp}_{2n}}$   .

On ratios of Petersson norms for Yoshida lifts