Skip to main content
×
Home

On the distribution of primes in short intervals

  • P. X. Gallagher (a1)
Abstract

One of the formulations of the prime number theorem is the statement that the number of primes in an interval (n, n + h], averaged over nN, tends to the limit λ, when N and h tend to infinity in such a way that hλ log N, with λ a positive constant.

Copyright
References
Hide All
1.Bombieri E. and Davenport H.. “Small differences between prime numbers”, Proc. Roy. Soc. Ser. A. 293 (1966), 118.
2.Halberstam H. and Richert E.. Sieve Methods (Academic Press, 1974).
3.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 Mathematica, 44 (1922), 170.
4.Hooley C.. “On the difference between consecutive numbers prime to n. II”, Publ. Math. Debrecen, 12 (1965), 3949.
5.Hooley C.. “On the intervals between consecutive terms of sequences”, Proc. Symp. Pure Math., 24 (1973), 129140.
6.Kendall M. G. and Stuart A.. The Advanced Theory of Statistics, Vol. I (Griffin, 1958).
7.Klimov N. I.. “Combination of elementary and analytic methods in the theory of numbers”, Uspehi Mat. Nauk, 13 (1958), no. 3 (81), 145164.
8.Lavrik A. F.. “On the theory of distribution of primes, based on I. M. Vinogradov's method of trigonometrical sums”, Trudy Mat. lnst. Sleklov., 64 (1961), 90125.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematika
  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 91 *
Loading metrics...

Abstract views

Total abstract views: 673 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 20th November 2017. This data will be updated every 24 hours.