Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-27T06:44:29.478Z Has data issue: false hasContentIssue false
  • English
  • Français

Some applications of Bombieri's theorem

Published online by Cambridge University Press:  26 February 2010

P. D. T. A. Elliott  and
H. Halberstam
P. D. T. A. Elliott
Affiliation:
University of Nottingham, University of Michigan
H. Halberstam
Affiliation:
University of Nottingham, University of Michigan
Get access

Extract

A famous conjecture of Hardy and Littlewood [4] stated that all sufficiently large integers n could be represented in the form

where p is a rational prime and x, y are integers. G. K. Stanley [9] showed that this result held for “almost all” integers n if one assumed a hypothesis concerning the zeros of L-functions similar to, though weaker than, the extended Riemann hypothesis.

Type
Research Article
Information
Mathematika , Volume 13 , Issue 2 , December 1966 , pp. 196 - 203
Copyright
Copyright © University College London 1966

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. Bombieri, E., “On the large sieve”, Mathematika, 12 (1965), 201–225.CrossRefGoogle Scholar
2. Bredekhin, B. M., “The dispersion method and binary additive problems”, see Russ. Math. Surveys, 20 (2), March-April (1965), 85–126.CrossRefGoogle Scholar
3. Estermann, T., “On an asymptotic formula due to Titchmarsh”, Journal London Math. Soc., 6 (1931), 250–251.CrossRefGoogle Scholar
4. Hardy, G. H. and Littlewood, J. E., “Some problems of partitio numerorum III. On the expression of a number as a sum of primes”, Acta Math., 44 (1922), 1–70.CrossRefGoogle Scholar
5. Hooley, C., “On the representation of a number as the sum of two squares and a prime”, Acta Math., 97 (1957), 189–210.CrossRefGoogle Scholar
6. Linnik, Yu. V., “An asymptotic formula in the Hardy-Littlewood additive problem”, Izv. Akad. Nauk SSSR, Ser. Mat., 24 (1960), 629–706.Google Scholar
7. Prachar, K., Primzahlverteilung (Springer, Berlin 1957).Google Scholar
8. Rodriques, G., “Sul problema dei divisori di Titchmareh”, Bollettino Unione Matematica Italiana (3), 20 (1965), 358–366.Google Scholar
9. Stanley, G. K., “On the representation of numbers as a sum of squares and primes”, Proc. London Math. Soc. (2), 29 (1928), 122–144.Google Scholar
10. Walfisz, A. Z., “On the theory of prime numbers”, Soobshch. Akad. Nauk Gruzin. SSR, 14 (1953), 77–83.Google Scholar