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
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