Almost all short intervals containing prime numbers

Chaohua Jia

Acta Arithmetica (1996)

  • Volume: 76, Issue: 1, page 21-84
  • ISSN: 0065-1036

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Chaohua Jia. "Almost all short intervals containing prime numbers." Acta Arithmetica 76.1 (1996): 21-84. <http://eudml.org/doc/206887>.

@article{ChaohuaJia1996,
author = {Chaohua Jia},
journal = {Acta Arithmetica},
keywords = {primes in short intervals; exponent 1/20},
language = {eng},
number = {1},
pages = {21-84},
title = {Almost all short intervals containing prime numbers},
url = {http://eudml.org/doc/206887},
volume = {76},
year = {1996},
}

TY - JOUR
AU - Chaohua Jia
TI - Almost all short intervals containing prime numbers
JO - Acta Arithmetica
PY - 1996
VL - 76
IS - 1
SP - 21
EP - 84
LA - eng
KW - primes in short intervals; exponent 1/20
UR - http://eudml.org/doc/206887
ER -

References

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  1. [1] H. Cramér, On the order of magnitude of the difference between consecutive prime numbers, Acta Arith. 2 (1937), 23-46. 
  2. [2] J.-M. Deshouillers and H. Iwaniec, Power mean values of the Riemann zeta-function, Mathematika 29 (1982), 202-212. 
  3. [3] G. Harman, Primes in short intervals, Math. Z. 180 (1982), 335-348. Zbl0482.10040
  4. [4] G. Harman, On the distribution of αp modulo one, J. London Math. Soc. (2) 27 (1983), 9-18. Zbl0504.10018
  5. [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. [6] D. R. Heath-Brown and H. Iwaniec, On the difference between consecutive primes, Invent. Math. 55 (1979), 49-69. Zbl0424.10028
  7. [7] M. N. Huxley, On the difference between consecutive primes, Invent. Math. 15 (1972), 164-170. Zbl0241.10026
  8. [8] H. Iwaniec, A new form of the error term in the linear sieve, Acta Arith. 37 (1980), 307-320. Zbl0444.10038
  9. [9] H. Iwaniec and J. Pintz, Primes in short intervals, Monatsh. Math. 98 (1984), 115-143. Zbl0544.10040
  10. [10] C. Jia, On Pjateckiĭ-Šapiro prime number theorem (II), Sci. China Ser. A 36 (1993), 913-926. Zbl0790.11063
  11. [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. [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. [13] C. Jia, On the exceptional set of Goldbach numbers in the short interval, Acta Arith., to appear. Zbl0863.11066
  14. [14] H. Li, On the Goldbach numbers in short interval, Sci. China Ser. A 38 (1995), 641-652. 
  15. [15] H. Li, Primes in short intervals, preprint. Zbl0875.11016
  16. [16] H. L. Montgomery, Topics in Multiplicative Number Theory, Lecture Notes in Math. 227, Springer, Berlin, 1971. Zbl0216.03501
  17. [17] Chengdong Pan and Chengbiao Pan, Goldbach Conjecture, Science Press, Beijing, 1981 (in Chinese). 
  18. [18] Chengdong Pan and Chengbiao Pan, The Basis of Analytic Number Theory, Science Press, Beijing, 1991 (in Chinese). 
  19. [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. Zbl0063.06869
  20. [20] N. Watt, Short intervals almost all containing primes, Acta Arith. 72 (1995), 131-167. Zbl0832.11030
  21. [21] N. Watt, Kloosterman sums and a mean value for Dirichlet polynomials, J. Number Theory, to appear. Zbl0837.11050

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