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Talk: An invitation to constant term sequences (Penn State)

An invitation to constant term sequences (Penn State)

Date: 2024/06/08
Occasion: The Legacy of Ramanujan 2024: Celebrating the 85th birthdays of George Andrews & Bruce Berndt
Place: Penn State University

Abstract

Many sequences in combinatorics and number theory can be represented as constant terms of powers of multivariate Laurent polynomials and, therefore, as diagonals of multivariate rational functions. On the other hand, it is an open question, raised by Don Zagier, to classify those diagonals which are constant terms. We provide such a classification in the case of sequences satisfying linear recurrences with constant coefficients. Various related examples, applications and open problems will be given as time permits. This talk is based on joint work with Alin Bostan and Sergey Yurkevich.

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