Series: Mathematics Colloquium

Date: Thursday, November 20, 2003

Time: 4:00 - 5:00 PM

Place: 102 McAllister Building

Host: George Andrews

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

Speaker: Kenneth B. Stolarsky, University of Illinois

Title: 

  q-Analogues, Conformal Mapping, Chebyshev Polynomials, and Prime
  Numbers

Abstract:  

  The study of discriminants of polynomials related to Chebyshev's led
  Karl Dilcher and the speaker most unexpectedly to multivariate
  inequalities related to conformal mappings.  This in turn led to a
  simple but novel way of generating q-analogues of "ordinary"
  functions, especially polynomials.  We examine these analogues both
  generally, and for Chebyshev polynomials in particular.  In one case
  they lead to a Pascal-type number triangle whose rows have a
  remarkable divisibility property that we have proved.  The speaker
  hopes to provide unexpected views of the topics listed in the title.