For more information about this meeting, contact Robert Vaughan.
| Title: | A partial theta identity of Ramanujan and its number theoretic interpretation |
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| Seminar: | Algebra and Number Theory Seminar |
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| Speaker: | Krishnaswami Alladi, University of Florida |
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| Abstract: |
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| 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 |
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| Date: | 12 / 04 / 2008 |
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| Time: | 11:15am - 12:05pm |
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