$\Lambda$-adic Families of Jacobi Forms

Matteo Longo; Marc-Hubert Nicole

$\Lambda$-adic Families of Jacobi Forms

Number Theory 2020-04-02 v3

Authors: Matteo Longo , Marc-Hubert Nicole

Abstract

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.

Keywords

p-adic analysis theta correspondence jacobi forms

Cite

@article{arxiv.1912.07920,
  title  = {$\Lambda$-adic Families of Jacobi Forms},
  author = {Matteo Longo and Marc-Hubert Nicole},
  journal= {arXiv preprint arXiv:1912.07920},
  year   = {2020}
}

Comments

22 pages, to appear in Research in Number Theory

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