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Electrostatic sieve

Published online by Cambridge University Press:  26 February 2010

Eugene L. Goldberg
Eugene L. Goldberg
Affiliation:
Department of Mathematics, Columbia University, New York, N.Y., U.S.A.
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Extract

In [1], P. X. Gallagher introduced a new sieve which is designed to produce better estimates than the large sieve when a vast number of congruence classes are chosen for each of the sieving primes. By making more explicit use of the principles underlying the sieve, these estimates can be improved and generalized to the case of complex quadratic fields. We shall see that the resulting estimates are best possible, if there are only a bounded number of unsieved classes per prime.

Type
Research Article
Information
Mathematika , Volume 23 , Issue 1 , June 1976 , pp. 51 - 56
Copyright
Copyright © University College London 1976

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References

1.Gallagher, P. X.. “A larger sieve”, Acta Arith., 18 (1971), 77–81.CrossRefGoogle Scholar
2.Szego, G.. Orthogonal Polynomials, revised edition (AMS Colloquium publications, 23, 1959).Google Scholar
3.Tsuji, M.. Potential Theory in Modern Function Theory (Maruzen, 1959).Google Scholar