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Jacobiformen und Thetareihen

Jacobiformen und Thetareihen We give a characterisation of Jacobi forms by classical modular forms from which we obtain dimension formulas for the spaces of Jacobi forms in certain cases. Then we consider the ordinary theta series to the quaternary quadratic forms of discriminant q2 (q an odd prime) representing 2; these possess a ‘natural’ continuation to Jacobi forms for which we give a sufficient condition of linear independence. If this condition is fulfilled and if there is no cusp form of weight 4 with respect to Γo(q) which vanishes at the cusp 0 with a certain order then the classical theta series are also linear independent. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Manuscripta Mathematica Springer Journals

Jacobiformen und Thetareihen

Manuscripta Mathematica , Volume 54 (3) – Jan 31, 2005

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References (21)

Publisher
Springer Journals
Copyright
Copyright © 1986 by Springer-Verlag
Subject
Mathematics; Mathematics, general; Algebraic Geometry; Topological Groups, Lie Groups; Geometry; Number Theory; Calculus of Variations and Optimal Control; Optimization
ISSN
0025-2611
eISSN
1432-1785
DOI
10.1007/BF01171338
Publisher site
See Article on Publisher Site

Abstract

We give a characterisation of Jacobi forms by classical modular forms from which we obtain dimension formulas for the spaces of Jacobi forms in certain cases. Then we consider the ordinary theta series to the quaternary quadratic forms of discriminant q2 (q an odd prime) representing 2; these possess a ‘natural’ continuation to Jacobi forms for which we give a sufficient condition of linear independence. If this condition is fulfilled and if there is no cusp form of weight 4 with respect to Γo(q) which vanishes at the cusp 0 with a certain order then the classical theta series are also linear independent.

Journal

Manuscripta MathematicaSpringer Journals

Published: Jan 31, 2005

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