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arXiv · 1304.3136

Effective Congruences for Mock Theta Functions

Nickolas Andersen·Holley Friedlander·Jeremy Fuller·Heidi Goodson
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Abstract

Let M(q)=\sum 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) \equiv 0 (mod \ell^j), where A is a multiple of \ell 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 prior works of Lichtenstein and Treneer.

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Nickolas Andersen, Holley Friedlander, Jeremy Fuller, Heidi Goodson. 2013-04-10. Effective Congruences for Mock Theta Functions. https://arxiv.org/abs/1304.3136

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