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Keywords = harmonic weak Maass forms

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11 pages, 201 KB  
Article
Effective Congruences for Mock Theta Functions
by Nickolas Andersen, Holley Friedlander, Jeremy Fuller and Heidi Goodson
Mathematics 2013, 1(3), 100-110; https://doi.org/10.3390/math1030100 - 4 Sep 2013
Cited by 2 | Viewed by 5577
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 [...] Read more.
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]. Full article
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