New Ramanujan-Kolberg type partition identities

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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Published 1 January 2002