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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 (CC BY 3.0).

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

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