Jacobi forms over totally real fields and codes over \(\mathbb F_p\)
type: Item
instance of: scholarly article
title: Jacobi forms over totally real fields and codes over \(\mathbb F_p\)
zbMATH Open document ID: 1020.11028
published in: Illinois Journal of Mathematics
publication date: 2002-12-16T00:00:00Z
review text: \textit{M. Broué} and \textit{M. Enguehard} [Ann. Sci. Éc. Norm. Supér. (4) 5, 157-181 (1972; Zbl 0254.94016)] studied a map between the space of invariant polynomials for a certain finite group and the ring of modular forms using the theta constants \(\theta_2(\tau)\) and \(\theta_3(\tau)\). This was generalized to codes over \(\mathbb F_p\) and Hilbert modular forms by \textit{W. Ebeling} [Lattices and codes. Braunschweig: Vieweg (1994; Zbl 0805.11048)]. In the paper under review the authors establish a connection between Hilbert-Jacobi forms over a totally real number field \(\mathbb Q(\zeta +\zeta^{-1})\), \(\zeta=e^{2\pi i/p}\), and codes over \(\mathbb F_p\) for an odd prime \(p\). In particular, they construct a theta series, which is a Jacobi form, from the complete weight enumerator or the Lee weight enumerator of a self-dual code over \(\mathbb F_p\).
Mathematics Subject Classification ID: 11F41
Mathematics Subject Classification ID: 11F50
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 11F27
Mathematics Subject Classification ID: 05E99
zbMATH DE Number: 1839966
zbMATH Keywords: theta series
zbMATH Keywords: Hilbert-Jacobi forms
zbMATH Keywords: Jacobi form
zbMATH Keywords: Lee weight enumerator
zbMATH Keywords: self-dual code
author: YoungJu Choie
author: Eun Kyung Jeong
reviewed by: Aloys Krieg
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1839966