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Quadratic Forms and Four Partition Functions Modulo 3

Jeremy Lovejoy / Robert Osburn
Published Online: 2011-02-24 | DOI: https://doi.org/10.1515/integ.2011.004


Recently, Andrews, Hirschhorn and Sellers have proven congruences modulo 3 for four types of partitions using elementary series manipulations. In this paper, we generalize their congruences using arithmetic properties of certain quadratic forms.

Keywords.: Partitions; overpartitions; congruences; binary quadratic forms; sums of squares

About the article

Received: 2010-09-16

Accepted: 2010-10-09

Published Online: 2011-02-24

Published in Print: 2011-02-01

Citation Information: Integers, Volume 11, Issue 1, Pages 47–53, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integ.2011.004.

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