# Meeting Details

Title: A partial theta identity of Ramanujan and its number theoretic interpretation Algebra and Number Theory Seminar Krishnaswami Alladi, University of Florida One of the most celebrated results in the theory of partitions and q-series is Euler's Pentagonal Numbers Theorem whose interpretation is that when the set partitions into distinct parts of an interger $n$ is split according to the parity of the number of parts, then the two subsets are of equal size except when $n$ is a pentagonal number, in which case the difference is 1. We will interpret a Ramanujan partial theta identity in a similar fashion, but here we are considering partitions into distinct parts with smallest part odd. Ramanujan's identity has an extra parameter which makes it deeper. We will give a novel proof of this. Our approach actually provides a companion to Ramanujan's identity which we will interpret combinatorially.