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

Effective Congruences for Mock Theta Functions

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; in revised form: 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

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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.

AMA Style

Andersen N, Friedlander H, Fuller J, Goodson H. Effective Congruences for Mock Theta Functions. Mathematics. 2013; 1(3):100-110.

Chicago/Turabian Style

Andersen, Nickolas; Friedlander, Holley; Fuller, Jeremy; Goodson, Heidi. 2013. "Effective Congruences for Mock Theta Functions." Mathematics 1, no. 3: 100-110.

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