Carlitz's q-analog of Bernoulli numbers as moments of orthogonal polynomials

Title:  Carlitz's q-analog of Bernoulli numbers as moments of orthogonal polynomials

Speaker:  Professor Jiang Zeng (Université Lyon 1)

Date:  Monday, 9th November 2015

Time:  4pm – 5pm

Location:  Agriculture. 1.01 (Seminar Room).

 

Abstract:


L. Carlitz introduced an interesting q-analog of the classical Bernoulli numbers in 1948. These rational functions have appeared recently in some different contexts of algebra and operator theory in relation with some q-zeta functions.  After recalling some basic properties  I will show  how  these q-Bernoulli numbers are related to the moments of some q-orthogonal polynomials. This connection yields then factorisations of several Hankel determinants of q-Bernoulli numbers, and continued fractions for their generating series. Some of these results are q-analogs of known results for Bernoulli numbers, but some are specific to the q-Bernoulli setting.


Series: Algebra and Number Theory