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arXiv · 1902.06429

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

Shih-Yu Chen·Atsushi Ichino
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Abstract

We prove an explicit formula for the Petersson norms of some normalized generic cuspidal newforms on ${\rm GSp}_4$ whose archimedean components belong to either discrete series representations or spherical principal series representations. Our formula expresses the Petersson norms in terms of special values of adjoint $L$-functions and some elementary constants depending only on local representations.

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Shih-Yu Chen, Atsushi Ichino. 2019-02-18. On Petersson norms of generic cusp forms and special values of adjoint $L$-functions for ${\rm GSp}_4$. https://arxiv.org/abs/1902.06429

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