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The large sieve inequality for algebraic number fields

Published online by Cambridge University Press:  26 February 2010

M. N. Huxley
M. N. Huxley
Affiliation:
St. John' College, Cambridge.
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Extract

The object of this paper is first to generalize the basic inequality of the large sieve method to exponential sums in many variables, and then to deduce results for algebraic number fields that are analogous to known results for the rational field.

Type
Research Article
Information
Mathematika , Volume 15 , Issue 2 , December 1968 , pp. 178 - 187
Copyright
Copyright © University College London 1968

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References

† “On the large sieve method”, Abhandlungen aus Zahlentheorie und Analysis zur Erinnerung an Edmund Landau (Berlin, 1968).Google Scholar

‡ ║x║ denotes the distance from a real number x to the nearest integer.

† This can be extended to a result involving a sum over squarefree ideals instead of prime ideals, on the lines of Montgomery, H. L.'s paper, J. London Math. Soc, 43 (1968), 93–98.CrossRefGoogle Scholar

† “The values of a trigonometrical polynomial at well spaced points”, Mathematika, 13 (1966), 91–96;CrossRefGoogle Scholar see also Corrigendum and Addendum, 14 (1967), 229–232.

† Gallagher, P. X., “The large sieve”, Mathematika, 14 (1967), 14'20.CrossRefGoogle Scholar