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Computing higher rank primitive root densities
P. Moree 1   ; P. Stevenhagen 2
1 Max-Planck-Institut für Mathematik Vivatsgasse 7 53111 Bonn, Germany
2 Mathematisch Instituut Universiteit Leiden Postbus 9512 2300 RA Leiden, The Netherlands
Acta Arithmetica, Tome 163 (2014) no. 1, pp. 15-32 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/aa163-1-2
Keywords: extend character sum method computation densities artin primitive root problems given lenstra authors situation radical extensions arbitrary rank algebraic set up identifies key parameters situation obviates lengthy analytic multiplicative number theory arguments computation actual densities yields conceptual interpretation formulas obtained enables extend their range application systematic

P. Moree  1   ; P. Stevenhagen  2

1 Max-Planck-Institut für Mathematik Vivatsgasse 7 53111 Bonn, Germany
2 Mathematisch Instituut Universiteit Leiden Postbus 9512 2300 RA Leiden, The Netherlands 
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P. Moree; P. Stevenhagen. Computing higher rank primitive root densities. Acta Arithmetica, Tome 163 (2014) no. 1, pp. 15-32. doi: 10.4064/aa163-1-2

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