Series: Mathematics Colloquium

Date: Thursday, November 6, 2003

Time: 4:00 - 5:00 PM

Place: 102 McAllister Building

Host: George Andrews

Refreshments: 3:15 - 4:00 PM, in 212 McAllister

Speaker: Krishnaswami Alladi, University of Florida

Title: 

New Weighted Rogers-Ramanujan Identities Mod 6 and 7 and Their
Analytic Representations

Abstract:  

In the entire theory of partitions and q-series, the Rogers-Ramanujan
identities are unmatched in simplicity, elegance, and depth.
Traditionally, the Rogers-Ramanujan partitions have always been
associated with the modulus 5.  By attaching multiplicative weights to
the Rogers-Ramanujan partitions, we show for the first time that they
are connected to moduli 6 and 7.  These weighted identities have
interesting analytic representations which have connections with
analytic identities due to Andrews and Bressoud, but the combinatorial
interpretation in these new analytic identities is more explicit.
This is joint work with Alexander Berkovich.  The talk will be
accessible to non-experts and students.