Primes in almost all short intervals

Alessandro Zaccagnini

Acta Arithmetica (1998)

  • Volume: 84, Issue: 3, page 225-244
  • ISSN: 0065-1036

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Alessandro Zaccagnini. "Primes in almost all short intervals." Acta Arithmetica 84.3 (1998): 225-244. <http://eudml.org/doc/207144>.

@article{AlessandroZaccagnini1998,
author = {Alessandro Zaccagnini},
journal = {Acta Arithmetica},
keywords = {primes; short intervals; almost all intervals; sieving},
language = {eng},
number = {3},
pages = {225-244},
title = {Primes in almost all short intervals},
url = {http://eudml.org/doc/207144},
volume = {84},
year = {1998},
}

TY - JOUR
AU - Alessandro Zaccagnini
TI - Primes in almost all short intervals
JO - Acta Arithmetica
PY - 1998
VL - 84
IS - 3
SP - 225
EP - 244
LA - eng
KW - primes; short intervals; almost all intervals; sieving
UR - http://eudml.org/doc/207144
ER -

References

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  1. [1] H. Halberstam and H. E. Richert, Sieve Methods, Academic Press, London, 1974. Zbl0298.10026
  2. [2] G. Harman, Primes in short intervals, Math. Z. 180 (1982), 335-348. Zbl0482.10040
  3. [3] D. R. Heath-Brown, Prime numbers in short intervals and a generalized Vaughan identity, Canad. J. Math. 34 (1982), 1365-1377. Zbl0478.10024
  4. [4] D. R. Heath-Brown, The number of primes in a short interval, J. Reine Angew. Math. 389 (1988), 22-63. Zbl0646.10032
  5. [5] M. N. Huxley, On the difference between consecutive primes, Invent. Math. 15 (1972), 164-170. Zbl0241.10026
  6. [6] C. Jia, Almost all short intervals containing prime numbers, Acta Arith. 76 (1996), 21-84. 
  7. [7] H. L. Montgomery, Topics in Multiplicative Number Theory, Lecture Notes in Math. 227, Springer, Berlin, 1971. Zbl0216.03501
  8. [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. Zbl0379.10023
  9. [9] P. Shiu, A Brun-Titchmarsh theorem for multiplicative functions, J. Reine Angew. Math. 313 (1980), 161-170. Zbl0412.10030
  10. [10] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, 2nd ed., Oxford Univ. Press, 1986. Zbl0601.10026
  11. [11] N. Watt, Kloosterman sums and a mean value for Dirichlet polynomials, J. Number Theory 53 (1995), 179-210. Zbl0837.11050
  12. [12] N. Watt, Short intervals almost all containing primes, Acta Arith. 72 (1995), 131-167. Zbl0832.11030
  13. [13] A. Zaccagnini, On the Selberg integral via Heath-Brown's identity, Riv. Mat. Univ. Parma 5 (1996), 205-212. Zbl0874.11065

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