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A CHARACTERIZATION OF MODIFIED MOCK THETA FUNCTIONS

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Abstract

We give a characterization of modified (in the sense of Zwegers) mock theta functions, parallel to that of ordinary theta functions. Namely, modified mock theta functions are characterized by their analyticity properties, elliptic transformation properties, and by being annihilated by certain second order differential operators.

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References

  1. P. Appell, Sur le fonctions doublement periodique de troisieme espece, Annals Sci. l'Ecole norm. Sup., 3e Sér. 1 (1884), 135–164; 2 (1885), 9–36; 3 (1886), 9–42.

  2. M. Gorelik, Weyl denominator identity for affine Lie superalgebras with non-zero dual Coxeter number, Jpn. J. Algebra 337 (2011), 50–62.

  3. M. Gorelik, V. G. Kac, Characters of (relatively) integrable modules over affine Lie superalgebras, Jpn. J. Math 10 (2015), no. 2, 135–235.

  4. V. G. Kac, Lie superalgebras, Adv. Math. 26 (1977), no. 1, 8–96.

  5. V. G. Kac, Infinite-Dimensional Lie Algebras, 3rd ed., Cambridge University Press, Cambridge, 1990. Russian transl.: Кaц, Бecкoнeчнoмepныe aлгeбpыЛи, Mиp, M., 1993.

  6. V. G. Kac, D. H. Peterson, Infinite-dimensional Lie algebras, theta functions and modular forms, Adv. Math. 53 (1984), 125–264.

  7. V. G. Kac, M. Wakimoto, Integrable highest weight modules over affine superalgebras and number theory, in: Lie Theory and Geometry, Progress in Math., Vol. 123, Birkhäuser Boston, Boston, MA, 1994, pp. 415–456.

  8. V. G. Kac, M. Wakimoto, Integrable highest weight modules over affine superalgebras and Appell's function, Commun. Math. Phys. 215 (2001), 631–682.

  9. V. G. Kac, M. Wakimoto, Representations of affine superalgebras and mock theta functions, Transform. Groups 19 (2014), 387–455.

  10. V. G. Kac, M. Wakimoto, Representations of affine superalgebras and mock theta functions II, Adv. Math. 300 (2016), DOI:10.1016/j.aim.2016.03.015.

  11. V. G. Kac, M. Wakimoto, Representations of affine superalgebras and mock theta functions III, Izv. Math 80 (2016), no. 4, DOI: 10.1070/IM8408.

  12. D. Mumford, Tata Lectures on Theta I, Progress in Math., Vol. 28, Birkhäuser Boston, Boston, MA, 1983. Russian transl.: Д. Maмфopд, Лeкции o mзmaфункцияx, Mиp, M., 1988.

  13. D. Zagier, Ramanujan's mock theta functions and their applications (after Zwegers and Ono–Bringmann), Seminaire Bourbaki, Vol. 2007/2008, Asterisque 326 (2009), Exp. no. 986 (2010), vii-viii, 143–164.

  14. S. P. Zwegers, Mock theta functions, arXiv:0807.4834 (2008).

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Authors and Affiliations

  1. Department of Mathematics, MIT, Cambridge, MA, 02139, USA

    VICTOR G. KAC

  2. 12-4 Karato-Rokkoudai, Kita-ku, Kobe, 651-1334, Japan

    MINORU WAKIMOTO

Authors
  1. VICTOR G. KAC
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  2. MINORU WAKIMOTO
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Correspondence to VICTOR G. KAC.

Additional information

*Supported in part by an NSF grant.

**Supported in part by Department of Mathematics, MIT.

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KAC, V.G., WAKIMOTO, M. A CHARACTERIZATION OF MODIFIED MOCK THETA FUNCTIONS. Transformation Groups 22, 979–1004 (2017). https://doi.org/10.1007/s00031-016-9403-8

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  • DOI: https://doi.org/10.1007/s00031-016-9403-8

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