Maass waveforms arising from sigma and related indefinite theta functions

Preprint English OPEN
Zwegers, Sander;
  • Subject: 11F27 | 11F03 | Mathematics - Number Theory
    acm: Hardware_GENERAL

In this paper we consider an example of a Maass waveform which was constructed by Cohen from a function $\sigma$, studied by Andrews, Dyson and Hickerson, and it's companion $\sigma^*$. We put this example in a more general framework.
  • References (8)

    [1] G. Andrews, F. Dyson and D. Hickerson, Partitions and indefinite quadratic forms, Invent. Math. 91 (1988), no. 3, pages 391-407.

    [2] K. Bringmann and B. Kane, Multiplicative q-hypergeometric series arising from real quadratic fields, Trans. Amer. Math. Soc., accepted for publication.

    [3] H. Cohen, q-identities for Maass waveforms, Invent. Math. 91 (1988), no. 3, pages 409-422.

    [4] D. Corson, D. Favero, K. Liesinger and S. Zubairy, Characters and q-series in Q(√2), J. Number Theory 107 (2004), pages 392-405.

    [5] J. Lovejoy, Overpartitions and real quadratic fields, J. Number Theory 106 (2004), pages 178-186.

    [6] A. Milton and I. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, 55 (1964).

    [7] M.-F. Vign´eras, S´eries thˆeta des formes quadratiques ind´efinies, in Modular functions of one variable VI (Proc. Second Internat. Conf., Univ. Bonn, Bonn, 1976), Lecture Notes in Math. 627, Springer, Berlin (1977), pages 227-239.

    [8] S. Zwegers, Mock theta functions, Ph.D. Thesis, Universiteit Utrecht (2002).

  • Metrics
Share - Bookmark