PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Robert Vaughan.

Title:A partial theta identity of Ramanujan and its number theoretic interpretation
Seminar:Algebra and Number Theory Seminar
Speaker:Krishnaswami Alladi, University of Florida
Abstract:
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.

Room Reservation Information

Room Number:MB106
Date:12 / 04 / 2008
Time:11:15am - 12:05pm