Mathematical Research Letters

Volume 9, Issue 6, November 2002 pp. 801-811.

New Ramanujan-Kolberg type partition identities

Authors: Heng Huat Chan, Heekyoung Hahn, Richard P. Lewis, and Siew Lian Tan
Author institution: National University of Singapore, University of Illinois at Urbana-Champaign, and University of Sussex

Summary: In this article, we use functions studied by N.J. Fine and R.J. Evans to construct analogues of modular equations first discovered by S. Ramanujan. We then use these functions to construct new identities satisfied by $\sum_{n=0}^\infty p(ln+k)q^n$, with odd prime $l$ and $0\leq k\leq (l-1)$. Our new partition identities are inspired by the work of O. Kolberg and Ramanujan.

Contents Full-Text PDF