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The average of the least primitive root

Published online by Cambridge University Press:  26 February 2010

D. A. Burgess  and
P. D. T. A. Elliott
D. A. Burgess
Affiliation:
Department of Mathematics, The University, Nottingham
P. D. T. A. Elliott
Affiliation:
Department of Mathematics, The University, Nottingham
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Extract

The problem of estimating accurately the order of magnitude of the least primitive root g(p) to a large prime modulus p is as yet unsolved. The first non-trivial estimate was obtained by I. M. Vinogradov (see [5]) who in about 1919 showed that

Type
Research Article
Information
Mathematika , Volume 15 , Issue 1 , June 1968 , pp. 39 - 50
Copyright
Copyright © University College London 1968

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References

1.Bombieri, E., “On the large sieve”, Mathematika, 12 (1965), 201–225.CrossRefGoogle Scholar
2.Burgess, D. A., “On character sums and primitive roots”, Proc. London Math. Soc. (3), 12 (1962), 179–192.CrossRefGoogle Scholar
3.Davenport, H. and Halberstam, H., “The values of a trigonometrical polynomial at well spaced points”, Mathematika, 13 (1966), 91–96; 14 (1967), 229–232.CrossRefGoogle Scholar
4.Gallagher, P. X., “The large sieve”, Mathematika, 14 (1967), 14–20.CrossRefGoogle Scholar
5.Landau, E., Vorlesungen über Zahlentheorie 2, 178 (Leipzig, 1927).Google Scholar
6.Prachar, K., Primzahlverteilung (Berlin, 1957).Google Scholar
7.Roth, K. F., “On the large sieves of Linnik and Rényi”, Mathematika, 12 (1965), 1–9.CrossRefGoogle Scholar
8.Turàn, P., “30 years of mathematics in the Soviet Union. Ill Results of number-theory in the Soviet Union”, Mat. Lapok 1 (1950), 243–266.Google Scholar
9.Wang, Y., “On the least primitive root of a prime”, Scientia Sinica, 10 (1961), No. 1.Google Scholar