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

Volume 213 / 2024

B. Adamczewski, J. P. Bell, É. Delaygue, F. Jouhet 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.

Authors

  • B. AdamczewskiUniv Lyon
    Université Claude Bernard Lyon 1
    CNRS UMR 5208
    Institut Camille Jordan
    F-69622 Villeurbanne, France
    e-mail
  • J. P. BellDepartment of Pure Mathematics
    University of Waterloo
    Waterloo, ON, Canada, N2L 3G1
    e-mail
  • É. DelaygueUniv Lyon
    Université Claude Bernard Lyon 1
    CNRS UMR 5208
    Institut Camille Jordan
    F-69622 Villeurbanne, France
    e-mail
  • F. JouhetUniv Lyon
    Université Claude Bernard Lyon 1
    CNRS UMR 5208
    Institut Camille Jordan
    F-69622 Villeurbanne, France
    e-mail

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