False theta functions and companions to Capparelli's identities |
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Authors: | Kathrin Bringmann Karl Mahlburg |
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Affiliation: | 1. Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany;2. Department of Mathematics, Louisiana State University, Baton Rouge, LA 70802, USA |
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Abstract: | Capparelli conjectured two modular identities for partitions whose parts satisfy certain gap conditions, which were motivated by the calculation of characters for the standard modules of certain affine Lie algebras and by vertex operator theory. These identities were subsequently proved and refined by Andrews, who related them to Jacobi theta functions, and also by Alladi–Andrews–Gordon, Capparelli and Tamba–Xie. In this paper we prove two new companions to Capparelli's identities, where the evaluations are expressed in terms of Jacobi theta functions and false theta functions. |
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Keywords: | 05A17 11P84 17B10 |
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