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arXiv · 2209.11075

Cyclotomic valuation of $q$-Pochhammer symbols and $q$-integrality of basic hypergeometric series

B. Adamczewski·J. P. Bell·É. Delaygue·F. Jouhet
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Abstract

We give a formula for the cyclotomic valuation of $q$-Pochhammer symbols in terms of (generalized) Dwork maps. We also obtain a criterion for the $q$-integrality of basic hypergeometric series in terms of certain step functions, which generalize Christol step functions. This provides suitable $q$-analogs of two results proved by Christol: a formula for the $p$-adic valuation of Pochhammer symbols and a criterion for the $N$-integrality of hypergeometric series.

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B. Adamczewski, J. P. Bell, É. Delaygue, F. Jouhet. 2022-09-22. Cyclotomic valuation of $q$-Pochhammer symbols and $q$-integrality of basic hypergeometric series. https://arxiv.org/abs/2209.11075

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