**On the representability of sequences as constant terms**

Alin Bostan, Armin Straub, Sergey Yurkevich — Preprint — 2022

## Abstract

A constant term sequence is a sequence of rational numbers whose \(n\)-th term is the constant term of \(P^n(\boldsymbol{x}) Q(\boldsymbol{x})\), where \(P(\boldsymbol{x})\) and \(Q(\boldsymbol{x})\) are multivariate Laurent polynomials. While the generating functions of such sequences are invariably diagonals of multivariate rational functions, and hence special period functions, it is a famous open question, raised by Don Zagier, to classify those diagonals which are constant terms. In this paper, we provide such a classification in the case of sequences satisfying linear recurrences with constant coefficients. We further consider the case of hypergeometric sequences and, for a simple illustrative family of hypergeometric sequences, classify those that are constant terms.## Download

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constantterms.pdf | 350.27 KB | Preprint (PDF, 24 pages) | 34 |

## BibTeX

@article{constantterms-2022, author = {Alin Bostan and Armin Straub and Sergey Yurkevich}, title = {On the representability of sequences as constant terms}, journal = {Preprint}, year = {2022}, }