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On the large sieve method in GF (q, x)

Published online by Cambridge University Press:  26 February 2010

John Johnsen
John Johnsen
Affiliation:
Department of Mathematics, University of Texas, Austin, Texas, 78712.
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Extract

The method of the large sieve has played a very important role in number theory. It turns out that estimates of exponential sums are of basic importance for large sieve inequalities. Let

be an exponential sum with complex coefficients c(n). It follows from Theorem 1 of Bombieri and Davenport [1] that

Type
Research Article
Information
Mathematika , Volume 18 , Issue 2 , December 1971 , pp. 172 - 184
Copyright
Copyright © University College London 1971

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References

1.Bombieri, E. and Davenport, H., “On the large sieve method ”, Abhandlungen aus Zahlentheorie und Analysis zur Erinnerung an Edmund Landau. Deutscher Verlag der Wissenschaften 1968, 11–12.Google Scholar
2.Gallagher, P. X., “The large sieve ”, Mathematika, 14 (1967), 14–20.CrossRefGoogle Scholar
3.Hayes, D. R., “The distribution of irreducibles in GF [q, x] ”, Trans. Amer. Math. Soc., 117 (1965), 101–127.Google Scholar
4.Montgomery, H. L., “A note on the large sieve ”, J . London Math. Soc., 43 (1968), 93–98.CrossRefGoogle Scholar
5.Lamprecht, E., “Gausssche Summen in endlichen kommutativen Ringen ”, Math. Nach., 9 (1953), 149–196.CrossRefGoogle Scholar