On the Distribution of Small Powers of a Primitive Root

C. I. Cobeli, S. M. Gonek, A. Zaharescu

Research output: Contribution to journalArticlepeer-review

Abstract

Let Ng={gn:1≤n≤N}, where g is a primitive root modulo an odd prime p, and let fg(m, H) denote the number of elements of Ng that lie in the interval (m, m+H], where 1≤m≤p. H. Montgomery calculated the asymptotic size of the second moment of fg(m, H) about its mean for a certain range of the parameters N and H and asked to what extent this range could be increased if one were to average over all the primitive roots (modp). We address this question as well as the related one of averaging over the prime p.

Original languageEnglish (US)
Pages (from-to)49-58
Number of pages10
JournalJournal of Number Theory
Volume88
Issue number1
DOIs
StatePublished - May 2001
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory

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