Hecke-Rogers double-sums and false theta functions

Abstract

We develop a setting in which one can evaluate certain Hecke-Rogers series in terms of false theta functions. We apply our setting to recent false theta function identities of Chan and Kim as well as Andrews and Warnaar.

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Acknowledgements

This research was supported by Ministry of Science and Higher Education of the Russian Federation, agreement No. 075-15-2019-1619, and by the Theoretical Physics and Mathematics Advancement Foundation BASIS, agreement No. 20-7-1-25-1.

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Correspondence to Eric T. Mortenson.

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Mortenson, E.T. Hecke-Rogers double-sums and false theta functions. Res. number theory 7, 28 (2021). https://doi.org/10.1007/s40993-021-00256-y

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Keywords

  • Hecke-Rogers double-sums
  • False theta functions
  • Mock theta functions

Mathematics Subject Classification

  • 11B65
  • 11F27