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On the large sieve inequality in an algebraic number field

Published online by Cambridge University Press:  26 February 2010

P. D. Schumer
P. D. Schumer
Affiliation:
Department of Mathematics Computer Science, Middlebury College, Middlebury, Vermont, 05753, U.S.A.
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Extract

Large sieve inequalities have been developed and applied to a host of arithmetical problems since their inception by Linnik in 1941. Such inequalities provide mean square estimates for a trigonometric polynomial over a set of well-spaced points. In particular, let x ∈ ℝ and let

Type
Research Article
Information
Mathematika , Volume 33 , Issue 1 , June 1986 , pp. 31 - 54
Copyright
Copyright © University College London 1986

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References

1.Davenport, H.. Multiplicative Number Theory, 2nd Edition (Springer, 1980).CrossRefGoogle Scholar
2.Gallagher, P. X.. The Large Sieve. Mathematika, 14 (1967), 14–20.CrossRefGoogle Scholar
3.Goldstein, L. J.. Analytic Number Theory (Prentice-Hall, Englewood Cliffs, 1971).Google Scholar
4.Goldstein, L. J.. On the Generalized Density Hypothesis, I. Analytic Number Theory, Lecture Notes 899 (Springer, 1981), 107–128.CrossRefGoogle Scholar
5.Goldstein, L. J.. On the Large Sieve Inequality in an Algebraic Number Field. Technical Report TR81-60 (University of Maryland, October 1981).Google Scholar
6.Hasse, H.. Zahlbericht (Physica-Verlag, Wurzberg-Wien, 1970).Google Scholar
7.Hecke, E.. Mathematische Werke (Vandehoek and Ruprecht, Göttingen, 1959), 178–185, 258–264.Google Scholar
8.Huxley, M. N.. The Large Sieve Inequality for Algebraic Number Fields. Mathematika, 15 (1968), 178–187.CrossRefGoogle Scholar
9.Huxley, M. N.. The Large Sieve Inequality for Algebraic Number Fields, II: Means of Moments of Hecke Zeta Functions. Proc. London Math. Soc., 31 (1970), 108–128.CrossRefGoogle Scholar
10.Huxley, M. N.. The Large Sieve Inequality for Algebraic Number Fields, III: Zero Density Results, Jour. London Math. Soc. (2), 3 (1971), 233–240.CrossRefGoogle Scholar
11.Lang, S.. Algebraic Number Theory (Addison-Wesley, Reading, 1970).Google Scholar
12.Lekkerkerker, C. G.. Geometry of Numbers (Wolters-Noordhofi, Amsterdam, 1969).Google Scholar
13.Montgomery, H.. Topics in Multiplicative Number Theory, Lecture Notes 227 (Springer, 1971).CrossRefGoogle Scholar
14.Montgomery, H.. Analytic Principle of the Large Sieve, Bull. Amer. Math. Soc. (4), 84 (1978), 547–567.CrossRefGoogle Scholar
15.Schaal, W.. On the Large Sieve Method in Algebraic Number Fields. J. of Number Theory, 2 (1970), 249–270.CrossRefGoogle Scholar
16.Siegel, C. L.. Abschatäung von Einheiten. Gesammelte Abhandlungen IV Springer, Berlin, (1979), 66–81.CrossRefGoogle Scholar
17.Wilson, R. J.. The Large Sieve in Algebraic Number Fields. Mathematika, 16 (1969), 189–204.CrossRefGoogle Scholar