Mathematical Research Letters

Volume 9 (2002)

Number 6

New Ramanujan-Kolberg type partition identities

Pages: 801 – 811

DOI: http://dx.doi.org/10.4310/MRL.2002.v9.n6.a8

Authors

Heng Huat Chan

Heekyoung Hahn

Richard P. Lewis

Siew Lian Tan

Abstract

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.

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