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\(\Lambda \)-adic families of Jacobi forms

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We show that Hida’s families of p-adic elliptic modular forms generalize to p-adic families of Jacobi forms. We also construct p-adic versions of theta lifts from elliptic modular forms to Jacobi forms. Our results extend to Jacobi forms previous works by Hida and Stevens on the related case of half-integral weight modular forms.

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Acknowledgements

Part of this work was done during visits of M.-H.N. at the Mathematics Department of the University of Padova whose congenial hospitality he is grateful for, and also during a visit of M.L. in Montréal supported by the grant of the CRM-Simons professorship held by M.-H.N. in 2017-2018 at the Centre de recherches mathématiques (C.R.M., Montréal).

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Longo, M., Nicole, MH. \(\Lambda \)-adic families of Jacobi forms. Res. number theory 6, 21 (2020). https://doi.org/10.1007/s40993-020-00196-z

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