Parity of the partition function and the modular discriminant

Wolfe, Sally

doi:10.2140/involve.2008.1.9

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Parity of the partition function and the modular discriminant

Sally Wolfe

Vol. 1 (2008), No. 1, 9–19

DOI: 10.2140/involve.2008.1.9

Abstract

We relate the parity of the partition function to the parity of the $q$ -series coefficients of certain powers of the modular discriminant using their generating functions. This allows us to make statements about the parity of the initial values of the partition function and to obtain a modified Euler recurrence for its parity.

Keywords

partition, congruences

Mathematical Subject Classification 2000

Primary: 05A17

Milestones

Received: 3 August 2007

Revised: 28 October 2007

Accepted: 28 October 2007

Published: 28 February 2008

Communicated by Ken Ono

Authors

Sally Wolfe
Department of Mathematics University of Wisconsin Madison, Wisconsin 53706 United States

Vol. 1, No. 1, 2008