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Bailey pairs and indefinite quadratic forms, II. False indefinite theta functions

Abstract

We construct families of Bailey pairs \((\alpha _n,\beta _n)\) where the exponent of q in \(\alpha _n\) is an indefinite quadratic form, but where the usual \((-1)^j\) is replaced by a sign function. This leads to identities involving “false” indefinite binary theta series. These closely resemble q-identities for mock theta functions or Maass waveforms, but the sign function prevents them from having the usual modular properties.

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Correspondence to Jeremy Lovejoy.

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Lovejoy, J. Bailey pairs and indefinite quadratic forms, II. False indefinite theta functions. Res. number theory 8, 24 (2022). https://doi.org/10.1007/s40993-022-00324-x

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  • DOI: https://doi.org/10.1007/s40993-022-00324-x

Keywords

  • Bailey pairs
  • False theta functions

Mathematics Subject Classification

  • 11F27
  • 33D15