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Quantum Jacobi forms in number theory, topology, and mathematical physics

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Abstract

We establish three infinite families of quantum Jacobi forms, arising in the diverse areas of number theory, topology, and mathematical physics, and unified by partial Jacobi theta functions.

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Notes

  1. We note that the same or similar notation for F and U appears in different sources (such as [6, 10, 20, 26, 41]) but may in reality define slightly different normalizations of these functions; the reader should proceed with caution when consulting the literature.

  2. Note that the function H defined here is not the same as the function with the same name in [34].

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Acknowledgements

The author thanks Kazuhiro Hikami and Jeremy Lovejoy for their helpful comments on an earlier version of this manuscript, and she is also thankful for the careful reading and helpful comments made by the referees of this paper. The author is grateful for the partial support of NSF Grant DMS-1901791 and NSF CAREER Grant DMS-1449679, and thanks the Simons Foundation Fellows in Mathematics Program, and the Institute for Advanced Study (Charles Simonyi Endowment), Princeton, for partial support provided during her sabbatical in 2018–2019.

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Folsom, A. Quantum Jacobi forms in number theory, topology, and mathematical physics. Res Math Sci 6, 25 (2019). https://doi.org/10.1007/s40687-019-0188-y

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