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Effective Congruences for Mock Theta Functions
Department of Mathematics, University of Illinois at Urbana-Champaign, 409 W. Green Street, Urbana, IL 61801, USA
Department of Mathematics, University of Massachusetts, Lederle Graduate Research Tower, Amherst, MA 01003, USA
Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907, USA
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
Abstract: Let M(q) = ∑c(n) qn 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 lj) 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  and Treneer .
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.
Andersen N, Friedlander H, Fuller J, Goodson H. Effective Congruences for Mock Theta Functions. Mathematics. 2013; 1(3):100-110.
Andersen, Nickolas; Friedlander, Holley; Fuller, Jeremy; Goodson, Heidi. 2013. "Effective Congruences for Mock Theta Functions." Mathematics 1, no. 3: 100-110.