\(p\)-adic aspects of Jacobi forms
type: Item
instance of: scholarly article
title: \(p\)-adic aspects of Jacobi forms
zbMATH Open document ID: 0878.11021
author: Adriana Sofer
published in: Journal of Number Theory
publication date: 1998-01-05T00:00:00Z
review text: The article concerns \(p\)-adic aspects of Jacobi forms. The author follows Serre's approach to \(p\)-adic modular forms, and defines the \(p\)-adic Jacobi forms (of a given weight) to be a limit of complex Jacobi forms [Definition 2.3; see also \textit{P. Guerzhoy}, Int. Math. Res. Not. 1994, No. 1, 31-39 (1994; Zbl 0869.11039)]. It turns out that \(p\)-adic Jacobi forms for \(\Gamma_0(p)\) are also forms for \(SL(2,\mathbb{Z})\) (theorem 2.4). The author associates to every Jacobi form with integral coefficients a measure on \(\mathbb{Z}_p\) with values in the \(p\)-adic ring of Katz's modular forms (theorem 3.1). It yields an injection and provides examples of \(p\)-adic analytic families of modular forms.
Mathematics Subject Classification ID: 11F33
Mathematics Subject Classification ID: 11F85
Mathematics Subject Classification ID: 11F50
zbMATH DE Number: 1011048
zbMATH Keywords: \(p\)-adic measure
zbMATH Keywords: Katz's \(p\)-adic modular forms
zbMATH Keywords: \(p\)-adic Jacobi forms
reviewed by: Andrzej Dąbrowski
MaRDI profile type: Publication
full work available at URL: jnth.1997.2095
OpenAlex ID: W2021915265
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DOI: 10.1006/JNTH.1997.2095
description: scientific article; zbMATH DE number 1011048