ArticleOriginal scientific text

Title

Primes in almost all short intervals

Authors 1

Affiliations

  1. Dipartimento di Matematica, Università di Parma, via Massimo d'Azeglio 85/a, 43100 Parma, Italy

Bibliography

  1. H. Halberstam and H. E. Richert, Sieve Methods, Academic Press, London, 1974.
  2. G. Harman, Primes in short intervals, Math. Z. 180 (1982), 335-348.
  3. D. R. Heath-Brown, Prime numbers in short intervals and a generalized Vaughan identity, Canad. J. Math. 34 (1982), 1365-1377.
  4. D. R. Heath-Brown, The number of primes in a short interval, J. Reine Angew. Math. 389 (1988), 22-63.
  5. M. N. Huxley, On the difference between consecutive primes, Invent. Math. 15 (1972), 164-170.
  6. C. Jia, Almost all short intervals containing prime numbers, Acta Arith. 76 (1996), 21-84.
  7. H. L. Montgomery, Topics in Multiplicative Number Theory, Lecture Notes in Math. 227, Springer, Berlin, 1971.
  8. B. Saffari and R. C. Vaughan, On the fractional parts of x/n and related sequences. II, Ann. Inst. Fourier (Grenoble) 27 (2) (1977), 1-30.
  9. P. Shiu, A Brun-Titchmarsh theorem for multiplicative functions, J. Reine Angew. Math. 313 (1980), 161-170.
  10. E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, 2nd ed., Oxford Univ. Press, 1986.
  11. N. Watt, Kloosterman sums and a mean value for Dirichlet polynomials, J. Number Theory 53 (1995), 179-210.
  12. N. Watt, Short intervals almost all containing primes, Acta Arith. 72 (1995), 131-167.
  13. A. Zaccagnini, On the Selberg integral via Heath-Brown's identity, Riv. Mat. Univ. Parma 5 (1996), 205-212.
Pages:
225-244
Main language of publication
English
Received
1997-03-26
Accepted
1997-06-24
Published
1998
Exact and natural sciences