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An average result for Artin's conjecture

Published online by Cambridge University Press:  26 February 2010

P. J. Stephens
P. J. Stephens
Affiliation:
Department of Mathematics, The University, Nottingham, NG7 2RD.
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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
Information
Mathematika , Volume 16 , Issue 2 , December 1969 , pp. 178 - 188
Copyright
Copyright © University College London 1969

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References

1.Hooley, C., “On Artin's conjecture”, Journal für Math., 225 (1967), 209–220.Google Scholar
2.Goldfeld, M., “Artin's conjecture on the average”, Mathematika, 15 (1968), 223–226.CrossRefGoogle Scholar
3.Turan, P., “On a theorem of Hardy and Ramanujan”, Journal London Math. Soc, 9 (1934), 274–276.Google Scholar
4.Prachar, K., Primzahlverteilung (Berlin, 1957).Google Scholar
5.Gallagher, P. X., “The large sieve”, Mathematika, 14 (1967), 14–20.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), 414–429.Google Scholar