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Computing higher rank primitive root densities

Volume 163 / 2014

P. Moree, P. Stevenhagen Acta Arithmetica 163 (2014), 15-32 MSC: Primary 11R45; Secondary 11L03, 11N13. DOI: 10.4064/aa163-1-2


We extend the “character sum method" for the computation of densities in Artin primitive root problems given by Lenstra and the authors to the situation of radical extensions of arbitrary rank. Our algebraic set-up identifies the key parameters of the situation at hand, and obviates the lengthy analytic multiplicative number theory arguments that used to go into the computation of actual densities. It yields a conceptual interpretation of the formulas obtained, and enables us to extend their range of application in a systematic way.


  • P. MoreeMax-Planck-Institut für Mathematik
    Vivatsgasse 7
    53111 Bonn, Germany
  • P. StevenhagenMathematisch Instituut
    Universiteit Leiden
    Postbus 9512
    2300 RA Leiden, The Netherlands

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