Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-08T07:55:57.407Z Has data issue: false hasContentIssue false

An average result for Artin's conjecture

Published online by Cambridge University Press:  26 February 2010

P. J. Stephens
Affiliation:
Department of Mathematics, The University, Nottingham, NG7 2RD.
Get access

Extract

Artin, in 1927, conjectured that for any given non-zero integer a other than — 1 or a perfect square there exist infinitely many primes for which a is a primitive root. He also conjectured that the number of primes not exceeding x, denoted by Na(x), for which a is a primitive root is given by the asymptotic formula

where A(a) is a constant depending on a.

Type
Research Article
Copyright
Copyright © University College London 1969

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Hooley, C., “On Artin's conjecture”, Journal für Math., 225 (1967), 209220.Google Scholar
2.Goldfeld, M., “Artin's conjecture on the average”, Mathematika, 15 (1968), 223226.CrossRefGoogle Scholar
3.Turan, P., “On a theorem of Hardy and Ramanujan”, Journal London Math. Soc, 9 (1934), 274276.Google Scholar
4.Prachar, K., Primzahlverteilung (Berlin, 1957).Google Scholar
5.Gallagher, P. X., “The large sieve”, Mathematika, 14 (1967), 1420.CrossRefGoogle Scholar
6.Landau, E., Vorlesungen iiber Zahlentheorie, Band 2 (Leipzig, 1927).Google Scholar
7.Titchmarsh, E. C., “A divisor problem”, Rend. Circ. Mat. Palermo, 54 (1930), 414429.Google Scholar