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An Improvement of a Large Sieve Inequality in High Dimensions

Part of: Sequences and sets

Published online by Cambridge University Press:  21 December 2009

Liangyi Zhao
Liangyi Zhao
Affiliation:
Department of Mathematics, University of Toronto, 40 Saint George Street, Toronto, ON M5S ZE4Canada. E-mail: lzhao@math.toronto.edu
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Abstract

In this paper, an improvement of a large sieve type inequality in high dimensions is presented, and its implications on a related problem are discussed.

MSC classification

Secondary: 11B57: Farey sequences; the sequences ${1^k, 2^k, cdots}$

Information

Type
Research Article
Information
Mathematika , Volume 52 , Issue 1-2 , December 2005 , pp. 93 - 100
Copyright
Copyright © University College London 2005

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References

1Barban, M. B., The “large sieve” method and its applications in the theory of numbers. Uspehi Matemat Nauk 21 (1966), 51–102.Google Scholar
2Bombieri, E., Le grand crible dans la théorie analytique des nombres. Société Math. France 18 (1974).Google Scholar
3Bombieri, E. and Davenport, H., Some inequalities involving trigonometrical polynomials. Annali Scuola Normale Superiore – Pisa 23 (1969), 223–241.Google Scholar
4Davenport, H. and Halberstam, H., The values of a trigonometric polynomial at well spaced points. Mathematika 13 (1966), 91–96 (Corrigendum and Addendum, Mathematika 14 (1967), 232–299).CrossRefGoogle Scholar
5Gallagher, P. X., The large sieve. Mathematika 14 (1967), 14–20.CrossRefGoogle Scholar
6Gallagher, P. X., The large sieve and probabilistic Galois theory. Proceedings of Symposium on Pure Mathematics, XXIV (American Mathematical Society, 1973), 91–101.Google Scholar
7Hardy, G. H., Littlewood, J. E., and Pólya, G., Inequalities. Cambridge University Press (1964).Google Scholar
8Huxley, M. N., The large sieve inequality for algebraic number fields. Mathematika 15 (1968), 178–187.CrossRefGoogle Scholar
9Knobloch, H.-W., Zum hilbertschen Irreduzibilitätssatz. Abh. Math. Sem. Univ. Hamburg. 19 (1955), 176–190.CrossRefGoogle Scholar
10Knobloch, H.-W., Die Seltenheit der reduziblen Polynome. Jber. Deutsch. Math. Verein 59 (1956), 12–19.Google Scholar
11Linnik, J. V., The large sieve. Doklady Akademii Nauk SSSR 36 (1941), 119–120 (Russian).Google Scholar
12Montgomery, H. L., Topics in Multiplicative Number Theory. Lecture Notes in Mathematics 227, (Spring-Verlag, Barcelona, etc., 1971).CrossRefGoogle Scholar
13Montgomery, H. L., The analytic principles of large sieve. Bull. Amer. Math. Soc. 84, 547–567.CrossRefGoogle Scholar
14Montgomery, H. L. and Vaughan, R. C., The large sieve. Mathematika 20 (1973), 119–134.CrossRefGoogle Scholar
15van der Waerden, B. L., Die Seltenheit der Gleichungen mit Affekt. Math. Ann. 109 (1934), 13–16.CrossRefGoogle Scholar
16Zhao, L., Large sieve inequality for characters to square moduli. Acta Arithmetica 112 (2004), 297–308.CrossRefGoogle Scholar
17Zhao, L., Large sieve inequality for special characters to prime square moduli. Functiones et Approximatio Commentarii Mathematici XXXII (2004), 99–106.Google Scholar