Cyclotomic valuation of $q$-Pochhammer symbols and $q$-integrality of basic hypergeometric series
Volume 213 / 2024
Acta Arithmetica 213 (2024), 131-167
MSC: Primary 33D15; Secondary 13A18, 33C20, 05A30
DOI: 10.4064/aa230428-19-9
Published online: 16 February 2024
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.
