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

Alin Bostan, Armin Straub, Sergey Yurkevich — Journal of Number Theory — Volume 253, 2023, Pages 235-256

## 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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## BibTeX

@article{constantterms-2023, author = {Alin Bostan and Armin Straub and Sergey Yurkevich}, title = {On the representability of sequences as constant terms}, journal = {Journal of Number Theory}, year = {2023}, volume = {253}, pages = {235--256}, doi = {10.1016/j.jnt.2023.06.015}, }