Effective Congruences for Mock Theta Functions

Nickolas Andersen, Holley Friedlander, Jeremy Fuller and Heidi Goodson
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Nickolas Andersen: Department of Mathematics, University of Illinois at Urbana-Champaign, 409 W. Green Street, Urbana, IL 61801, USA
Holley Friedlander: Department of Mathematics, University of Massachusetts, Lederle Graduate Research Tower, Amherst, MA 01003, USA
Jeremy Fuller: Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907, USA
Heidi Goodson: Department of Mathematics, University of Minnesota, 206 Church St. SE, Minneapolis, MN 55455, USA

Mathematics, 2013, vol. 1, issue 3, 1-11

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 ( A n + 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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2013
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