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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Zhu reduction for Jacobi $n$-point functions and applications
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by Kathrin Bringmann, Matthew Krauel and Michael Tuite PDF
Trans. Amer. Math. Soc. 373 (2020), 3261-3293


We establish precise Zhu reduction formulas for Jacobi $n$-point functions which show the absence of any possible poles arising in these formulas. We then exploit this to produce results concerning the structure of strongly regular vertex operator algebras, and also to motivate new differential operators acting on Jacobi forms. Finally, we apply the reduction formulas to the Fermion model in order to create polynomials of quasi-Jacobi forms which are Jacobi forms.
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Additional Information
  • Kathrin Bringmann
  • Affiliation: Institute of Mathematics, University of Cologne, Albertus-Magnus-Platz, 50923 Köln, Germany
  • MR Author ID: 774752
  • Email:
  • Matthew Krauel
  • Affiliation: Department of Mathematics and Statistics, California State University, Sacramento, California 95819
  • MR Author ID: 982089
  • Email:
  • Michael Tuite
  • Affiliation: School of Mathematics, Statistics and Applied Mathematics, National University of Ireland Galway, University Road, Galway, Ireland H91 TK33
  • MR Author ID: 175150
  • ORCID: 0000-0002-7352-4556
  • Email:
  • Received by editor(s): October 11, 2018
  • Received by editor(s) in revised form: August 10, 2019
  • Published electronically: February 11, 2020
  • Additional Notes: Research of the first author was supported by the Alfried Krupp Prize for Young University Teachers of the Krupp foundation and the research leading to these results received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant agreement n. 335220 - AQSER
    Research of the second author for this project was supported by the European Research Council (ERC) Grant agreement n. 335220 - AQSER, and also by a research visit to the Max Plank Institute for Mathematics in Bonn
  • © Copyright 2020 by the authors
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 3261-3293
  • MSC (2010): Primary 11F50, 17B69
  • DOI:
  • MathSciNet review: 4082238