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Effective Congruences for Mock Theta Functions

Author

Listed:
  • Nickolas Andersen

    (Department of Mathematics, University of Illinois at Urbana-Champaign, 409 W. Green Street, Urbana, IL 61801, USA)

  • Holley Friedlander

    (Department of Mathematics, University of Massachusetts, Lederle Graduate Research Tower, Amherst, MA 01003, USA)

  • Jeremy Fuller

    (Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907, USA)

  • Heidi Goodson

    (Department of Mathematics, University of Minnesota, 206 Church St. SE, Minneapolis, MN 55455, USA)

Abstract

Let M ( q ) = ∑ c(n)q n be one of Ramanujan’s mock theta functions. We establish the existence of infinitely many linear congruences of the form: c ( A n + B ) ≡ 0 (mod l j ) where A is a multiple of l and an auxiliary prime, p. Moreover, we give an effectively computable upper bound on the smallest such p for which these congruences hold. The effective nature of our results is based on the prior works of Lichtenstein [1] and Treneer [2].

Suggested Citation

  • Nickolas Andersen & Holley Friedlander & Jeremy Fuller & Heidi Goodson, 2013. "Effective Congruences for Mock Theta Functions," Mathematics, MDPI, vol. 1(3), pages 1-11, September.
    • Handle: RePEc:gam:jmathe:v:1:y:2013:i:3:p:100-110:d:28556
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