Next Article in Journal
Previous Article in Journal
Mathematics 2013, 1(3), 100-110; doi:10.3390/math1030100
Article

Effective Congruences for Mock Theta Functions

1
, 2
, 3
 and 4,*
Received: 18 July 2013; in revised form: 27 August 2013 / Accepted: 27 August 2013 / Published: 4 September 2013
Download PDF [201 KB, uploaded 4 September 2013]
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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Export to BibTeX |
EndNote


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.

Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert