Theta function transformation formulas and the Weil representation
type: Item
instance of: scholarly article
title: Theta function transformation formulas and the Weil representation
zbMATH Open document ID: 0566.10020
DOI: 10.1016/0022-314X(85)90032-0
author: Solomon Friedberg
published in: Journal of Number Theory
publication date: 1985-01-01T00:00:00Z
review text: This paper establishes a new connection between the Weil representation of the metaplectic cover of Sp(2,\({\mathbb{R}})\) and the corresponding Siegel theta functions on the Siegel half-space. The Weil representation is equipped with a linear functional which gives rise in a standard way to the theta functions. The author reverses this process and represents the linear functional as a limit of functionals formed by integrating against the theta function. From this representation he is able to deduce the invariance properties of the functional from those of the theta function.
Mathematics Subject Classification ID: 11F27
zbMATH DE Number: 3902748
zbMATH Keywords: explicit determination of eigth root of unity
zbMATH Keywords: invariance of theta functional
zbMATH Keywords: Weil representation
zbMATH Keywords: metaplectic cover of Sp(2,\({\mathbb{R}})\)
zbMATH Keywords: Siegel theta functions
reviewed by: Samuel James Patterson
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3902748