ArticleOriginal scientific text

Title

Almost all short intervals containing prime numbers

Authors 1

Affiliations

  1. Institute of Mathematics, Academia Sinica, Beijing, 100080, China

Bibliography

  1. H. Cramér, On the order of magnitude of the difference between consecutive prime numbers, Acta Arith. 2 (1937), 23-46.
  2. J.-M. Deshouillers and H. Iwaniec, Power mean values of the Riemann zeta-function, Mathematika 29 (1982), 202-212.
  3. G. Harman, Primes in short intervals, Math. Z. 180 (1982), 335-348.
  4. G. Harman, On the distribution of αp modulo one, J. London Math. Soc. (2) 27 (1983), 9-18.
  5. D. R. Heath-Brown, Finding primes by sieve methods, Proc. 1982 ICM, Warsaw, 1983, Vol. 1, PWN-Polish Sci. Publ., Warszawa, 1984, 487-492.
  6. D. R. Heath-Brown and H. Iwaniec, On the difference between consecutive primes, Invent. Math. 55 (1979), 49-69.
  7. M. N. Huxley, On the difference between consecutive primes, Invent. Math. 15 (1972), 164-170.
  8. H. Iwaniec, A new form of the error term in the linear sieve, Acta Arith. 37 (1980), 307-320.
  9. H. Iwaniec and J. Pintz, Primes in short intervals, Monatsh. Math. 98 (1984), 115-143.
  10. C. Jia, On Pjateckiĭ-Šapiro prime number theorem (II), Sci. China Ser. A 36 (1993), 913-926.
  11. C. Jia, Goldbach numbers in short interval, Sci. China Ser. A 24 (1994), 1233-1259 (in Chinese); I. Sci. China Ser. A 38 (1995), 385-406; II. Sci. China Ser. A 38 (1995), 513-523.
  12. C. Jia, On the difference between consecutive primes, Sci. China Ser. A 25 (1995), 785-804 (in Chinese); Sci. China Ser. A 38 (1995), 1163-1186.
  13. C. Jia, On the exceptional set of Goldbach numbers in the short interval, Acta Arith., to appear.
  14. H. Li, On the Goldbach numbers in short interval, Sci. China Ser. A 38 (1995), 641-652.
  15. H. Li, Primes in short intervals, preprint.
  16. H. L. Montgomery, Topics in Multiplicative Number Theory, Lecture Notes in Math. 227, Springer, Berlin, 1971.
  17. Chengdong Pan and Chengbiao Pan, Goldbach Conjecture, Science Press, Beijing, 1981 (in Chinese).
  18. Chengdong Pan and Chengbiao Pan, The Basis of Analytic Number Theory, Science Press, Beijing, 1991 (in Chinese).
  19. A. Selberg, On the normal density of primes in short intervals, and the difference between consecutive primes, Arch. Math. Naturvid. 47 (1943), 87-105.
  20. N. Watt, Short intervals almost all containing primes, Acta Arith. 72 (1995), 131-167.
  21. N. Watt, Kloosterman sums and a mean value for Dirichlet polynomials, J. Number Theory, to appear.
Pages:
21-84
Main language of publication
English
Received
1995-03-29
Published
1996
Exact and natural sciences