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We prove an explicit formula for the Petersson norms of some normalizedgeneric cuspidal newforms on ${\rm GSp}_4$ whose archimedean components belongto either discrete series representations or spherical principal seriesrepresentations. Our formula expresses the Petersson norms in terms of specialvalues of adjoint $L$-functions and some elementary constants depending only onlocal representations.

On Petersson norms of generic cusp forms and special values of adjoint $L$-functions for ${\rm GSp}_4$