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On the distribution of primes in short intervals

  • P. X. Gallagher (a1)
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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.

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References
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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.
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Mathematika
  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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