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|
|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
|Date:||12 / 04 / 2008|
|Time:||11:15am - 12:05pm|