Next Article in Journal
Sign-Periodicity of Traces of Singular Moduli
Previous Article in Journal
Scattering of Electromagnetic Waves by Many Nano-Wires
Article Menu

Export Article

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

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 / Revised: 27 August 2013 / Accepted: 27 August 2013 / Published: 4 September 2013
View Full-Text   |   Download PDF [201 KB, uploaded 4 September 2013]


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]. View Full-Text
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 (CC BY 3.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

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

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top