Mathematical Research Letters

Volume 9 (2002)

Number 6

New Ramanujan-Kolberg type partition identities

Pages: 801 – 811



Heng Huat Chan

Heekyoung Hahn

Richard P. Lewis

Siew Lian Tan


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.

Full Text (PDF format)