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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2022

On the representability of sequences as constant terms

Résumé

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.
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Dates et versions

hal-03907115 , version 1 (19-12-2022)
hal-03907115 , version 2 (22-12-2022)

Identifiants

Citer

Alin Bostan, Armin Straub, Sergey Yurkevich. On the representability of sequences as constant terms. 2022. ⟨hal-03907115v1⟩
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