On the average number of elements in a finite field with order or index in a prescribed residue class

  • Authors:

  • Pieter Moree

  • Affiliations:

  • Faculty of Science, Korteweg-de Vries Institute for Mathematics, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands

  • Venue:
  • Finite Fields and Their Applications
  • Year:
  • 2004

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Abstract

For any prime p the density of elements in F"p^* having order, respectively index, congruent to a(modd) is being considered. These densities on average are determined, where the average is taken over all finite fields of prime order. Some connections between the two densities are established. It is also shown how to compute these densities with high numerical accuracy.