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Fourier–Jacobi periods of classical Saito–Kurokawa lifts

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Abstract

Kohnen–Skoruppa (Invent Math 95(3): 541–558, 1989) proved a formula for the ratio of the Petersson inner products of the half integral weight modular form and its Saito–Kurokawa lifting. We give an interpretation of this formula in the framework of the refined Gan–Gross–Prasad conjecture. This provides us with an example of the refined Gan–Gross–Prasad conjecture for the nontempered representations.

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Acknowledgments

I thank Atsushi Ichino for some helpful discussions.

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Authors and Affiliations

  1. School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, 08540, NJ, USA

    Hang Xue

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  1. Hang Xue
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Correspondence to Hang Xue.

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This material is based upon work supported by the National Science Foundation under agreement No. DMS-1128115.

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Xue, H. Fourier–Jacobi periods of classical Saito–Kurokawa lifts. Ramanujan J 45, 111–139 (2018). https://doi.org/10.1007/s11139-016-9829-6

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  • DOI: https://doi.org/10.1007/s11139-016-9829-6

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