Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-28T05:03:35.513Z Has data issue: false hasContentIssue false
  • English
  • Français

The distribution of polynomial sequences

Published online by Cambridge University Press:  26 February 2010

H. Halberstam  and
H.-E. Richert
H. Halberstam
Affiliation:
Mathematics Department, University of Nottingham.
H.-E. Richert
Affiliation:
Abteilung för Mathematik, Universität Ulm, Germany.
Get access

Extract

Prime number theory is concerned with the distribution of primes in sequences of natural numbers, such as arithmetic progressions or polynomial sequences. An extensive range of such questions is embraced by

Hypothesis H (Schinzel, see [10]. Let f1, …, fgbe distinct irreducible polynomials in Z[x] (with positive leading coefficients) and suppose that f1 …fghas no fixed prime divisors. Then there exist infinitely many integers n such that each fi (n) (i = 1, …, g) is prime.

Type
Research Article
Information
Mathematika , Volume 19 , Issue 1 , June 1972 , pp. 25 - 50
Copyright
Copyright © University College London 1972

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 Horn, R. A., Mathem. Comp., 16 (1962), 363–367.CrossRefGoogle Scholar
3.Bombieri, E., Mathematika, 12 (1965), 201–225.CrossRefGoogle Scholar
4.Buchstab, A. A., Doklady Akad. Nauk, SSSR 162 (1965), 735–738.Google Scholar
5.Halberstam, H. and Richert, H.-E.Sieve Methods (to be published by Markham Publishing Co., Chicago).Google Scholar
6.Miech, R. J., Ada Arith., 11 (1965), 35–56.CrossRefGoogle Scholar
7.Nagel, T., J. de Mathematiques (8), 4 (1921), 343–356.Google Scholar
8.Porter, J. W., Acta Arith. (to appear).Google Scholar
9.Richert, H.-E., Mathematika, 16(1969), 1–22.Google Scholar
10.Schinzel, A. and Sierpinski, W., Acta Arith., 4 (1958), 185–208.Google Scholar
11.Selberg, A., Skand. Math. Kongr., 11 (1949), 13–22.Google Scholar