Λ-ADIC FAMILIES OF JACOBI FORMS

Matteo Longo (1) , Marc-Hubert Nicole (2, 3)

1 Dipartimento di Matematica [padova]
2 I2M - Institut de Mathématiques de Marseille
3 IRL CRM-CNRS - International Research Lab

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.

Domaines: Théorie des nombres [math.NT]; Géométrie algébrique [math.AG]

Matteo Longo, Marc-Hubert Nicole. Λ-ADIC FAMILIES OF JACOBI FORMS. Research in Number Theory, 2020, 6 (2), pp.21. ⟨hal-01798750v2⟩