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

2022/09/22 by Adamczewski, B., Bell, J. P., Delaygue, É. +1
#05A30 (Secondary) #13A18 (Primary) 33C20 #33D15 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2209.11075

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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