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Pré-Publication, Document De Travail Année : 2022

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

Boris Adamczewski
Jason P. Bell
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Eric Delaygue

Résumé

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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Dates et versions

hal-03783937 , version 1 (22-09-2022)

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  • HAL Id : hal-03783937 , version 1

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Boris Adamczewski, Jason P. Bell, Eric Delaygue, Frédéric Jouhet. Cyclotomic valuation of q-Pochhammer symbols and q-integrality of basic hypergeometric series. 2022. ⟨hal-03783937⟩
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