Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-10T16:57:18.929Z Has data issue: false hasContentIssue false
  • English
  • Français

Selberg's sieve with weights

Published online by Cambridge University Press:  26 February 2010

H.-E. Richert
H.-E. Richert
Affiliation:
University of Marburg and Syracuse University
Get access

Extract

Let be a (finite) non-empty sequence of integers, and let K be a positive integer. The aim of the Brun-Selberg sieve is to obtain bounds for the “sifting function”

where z ≥ 2 is a real number and

Type
Research Article
Information
Mathematika , Volume 16 , Issue 1 , June 1969 , pp. 1 - 22
Copyright
Copyright © University College London 1969

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Ankeny, N. C. and Onishi, H., Ada Arith., 10 (1964), 31–62.CrossRefGoogle Scholar
2.Bateman, P. T. and Stemmler, R. M., Illinois J. Math., 6 (1962), 142–156.Google Scholar
3.Bombieri, E., Mathematika, 12 (1965), 201–225.CrossRefGoogle Scholar
4.Brun, V., Norske Vid. Selsk. Skrifter., I. M.-N. Kl., Kristiania, 3 (1920), 1–36.Google Scholar
5.Buchstab, A. A., Doklady Akad. Nauk SSSR, 162 (1965), 735–738 = Soviet Math. Doklady, 6 (1965), 729–732.Google Scholar
6.Buchstab, A. A., Uspehi Mat. Nauk, 22: 3 (135) (1967), 199–226 = Russian Math. Surveys, 22: 3 (1967), 205–233.Google Scholar
7.Fluch, W., Ada Arith., 5 (1959), 381–405.CrossRefGoogle Scholar
8.Halberstam, H., Jurkat, W. B. and Richert, H.-E., C. R. Acad. Sc. Paris, 264 (1967), 920–923.Google Scholar
9.Halberstam, H., and Richert, H.-E., Sieve methods (to be published by Markham Publishing Co., Chicago).CrossRefGoogle Scholar
10.Jurkat, W. B. and Richert, H.-E., Ada Arith., 11 (1965), 217–240.CrossRefGoogle Scholar
11.Kuhn, P., Norske Vid. Selsk. Forh., Trondheim, 14, No. 39 (1941), 145–148.Google Scholar
12.Kuhn, P., 12. Skand. Mat. Kongr. Lund 1953, 160–168.Google Scholar
13.Levin, B. V., Acta Arith., 10 (1964/1965), 387–397.CrossRefGoogle Scholar
14.Miech, R. J., Acta Arith., 10 (1964). 9–30.CrossRefGoogle Scholar
15.Miech, R. J., Acta Arith., 11 (1965), 35–56.CrossRefGoogle Scholar
16.Nagel, T., Journal de Mathématiques (8), 4 (1921), 343–356.Google Scholar
17.Rademacher, H., Abh. Hamburg, 3 (1924), 12–30.CrossRefGoogle Scholar
18.Rényi, A., Izvestija Akad. Nauk SSSR, Ser. Mat., 12 (1948), 57–78 = Translations Amer. Math. Soc, (2) 19 (1962), 299–321.Google Scholar
19.Ricci, G., Annali della R. Scuola Normale Superiore di Pisa (2), 6 (1937), 71–116.Google Scholar
20.Wang, Y., Science Record, N.S., 1 (1957), No. 3, 1–5.Google Scholar
21.Wang, Y., Scientia Sinica, 11 (1962), 1607–1624.Google Scholar