On the pseudo-randomness of subsets related to primitive roots

Cécile Dartyge, András Sárközy, Mihály Szalay

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Many results have been proved on the distribution of the primitive roots. These results reflect certain random type properties of the set Gp of the primitive roots modulo p. This fact motivates the question that in what extent behaves Gp as a random subset of ℤp? First a much more general form of this problem is studied by using the notion of pseudo-randomness of subsets of ℤn which has been introduced and studied recently by Dartyge and Sárközy. This is followed by the study of the pseudo-randomness of a subset of ℤp defined by index properties. In both cases it turns out that these subsets possess strong pseudo-random properties (the well-distribution measure and correlation measure of order k are small) but the pseudo-randomness is not perfect: there is a pseudo-random measure (the symmetry measure) which is large.

Original languageEnglish
Pages (from-to)139-162
Number of pages24
JournalCombinatorica
Volume30
Issue number2
DOIs
Publication statusPublished - Sep 24 2010

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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