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On two fifth order mock theta functions

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Abstract

We consider the fifth order mock theta functions χ 0 and χ 1, defined by Ramanujan, and find identities for these functions, which relate them to indefinite theta functions. Similar identities have been found by Andrews for the other fifth order mock theta functions and the seventh order functions.

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References

  1. Andrews, G.E.: Mock theta functions. In: Theta Functions—Bowdoin 1987, Part 2, Brunswick, 1987. Proc. Symp. Pure Math., vol. 49, pp. 283–298. Am. Math. Soc., Providence (1989)

    Google Scholar 

  2. Andrews, G.E.: The fifth and seventh order mock theta functions. Trans. Am. Math. Soc. 293(1), 113–134 (1986)

    Article  MATH  Google Scholar 

  3. Andrews, G.E.: q-Series: Their Development and Application in Analysis, Number Theory, Combinatories, Physics, and Computer Algebra. CBMS Regional Conf. Ser. in Math., vol. 66. Am. Math. Soc., Providence (1986)

    Google Scholar 

  4. Bringmann, K., Ono, K.: Dyson’s ranks and Maass forms. Ann. Math. (to appear)

  5. Ramanujan, S.: The Lost Notebook and Other Unpublished Papers. Narosa Publishing House, New Delhi (1987)

    Google Scholar 

  6. Zagier, D.B.: Ramanujan’s mock theta functions and their applications. Séminaire Bourbaki, no. 986 (2007–2008)

  7. Zwegers, S.P.: Theta functions for quadratic forms of type (r,1) and mock theta functions (in preparation)

  8. Zwegers, S.P.: Mock ϑ-functions and real analytic modular forms. In: q-Series with Applications to Combinatorics, Number Theory, and Physics. Contemporary Mathematics, vol. 291, pp. 269–277. Am. Math. Soc., Providence (2001)

    Google Scholar 

  9. Zwegers, S.P.: Mock theta functions. Ph.D. Thesis, Utrecht University (2002). http://igitur-archive.library.uu.nl/dissertations/2003-0127-094324/inhoud.htm

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  1. School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland

    Sander Zwegers

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  1. Sander Zwegers
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Correspondence to Sander Zwegers.

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Zwegers, S. On two fifth order mock theta functions. Ramanujan J 20, 207–214 (2009). https://doi.org/10.1007/s11139-008-9138-9

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  • DOI: https://doi.org/10.1007/s11139-008-9138-9

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