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Mathematics 2013, 1(3), 100-110; doi:10.3390/math1030100
Article

Effective Congruences for Mock Theta Functions

1
, 2
, 3
 and 4,*
1 Department of Mathematics, University of Illinois at Urbana-Champaign, 409 W. Green Street, Urbana, IL 61801, USA 2 Department of Mathematics, University of Massachusetts, Lederle Graduate Research Tower, Amherst, MA 01003, USA 3 Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907, USA 4 Department of Mathematics, University of Minnesota, 206 Church St. SE, Minneapolis, MN 55455, USA
* Author to whom correspondence should be addressed.
Received: 18 July 2013 / Revised: 27 August 2013 / Accepted: 27 August 2013 / Published: 4 September 2013
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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(An + 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].
Keywords: mock theta functions; congruences; harmonic weak Maass forms mock theta functions; congruences; harmonic weak Maass forms
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Andersen, N.; Friedlander, H.; Fuller, J.; Goodson, H. Effective Congruences for Mock Theta Functions. Mathematics 2013, 1, 100-110.

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