Limitations to the equi-distribution of primes III

John Friedlander; Andrew Granville

Compositio Mathematica (1992)

  • Volume: 81, Issue: 1, page 19-32
  • ISSN: 0010-437X

How to cite


Friedlander, John, and Granville, Andrew. "Limitations to the equi-distribution of primes III." Compositio Mathematica 81.1 (1992): 19-32. <>.

author = {Friedlander, John, Granville, Andrew},
journal = {Compositio Mathematica},
keywords = {prime numbers; arithmetic progressions; Omega results; Maier's method},
language = {eng},
number = {1},
pages = {19-32},
publisher = {Kluwer Academic Publishers},
title = {Limitations to the equi-distribution of primes III},
url = {},
volume = {81},
year = {1992},

AU - Friedlander, John
AU - Granville, Andrew
TI - Limitations to the equi-distribution of primes III
JO - Compositio Mathematica
PY - 1992
PB - Kluwer Academic Publishers
VL - 81
IS - 1
SP - 19
EP - 32
LA - eng
KW - prime numbers; arithmetic progressions; Omega results; Maier's method
UR -
ER -


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  2. [Bu] A.A. Buchstab: On an asymptotic estimate of the number of numbers of an arithmetic progression which are not divisible by relatively small prime numbers, Mat. Sb.28 (70) (1951), 165-184 (in Russian). MR45756
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  5. [FGHM] J. Friedlander, A. Granville, A. Hildebrand, and H. Maier: Oscillation theorems for primes in arithmetic progressions and for sifting functions, to appear in J. Amer. Math. Soc. Zbl0724.11040MR1080647
  6. [Ga] P.X. Gallagher: A large sieve density estimate near σ = 1, Invent. Math.11 (1970), 329-339. Zbl0219.10048
  7. [HRi] H. Halberstam and H.-E. Richert: Sieve Methods, L.M.S. Monographs, Academic Press, London (1974). Zbl0298.10026MR424730
  8. [HRa] G.H. Hardy and S. Ramanujan: The normal number of prime factors of a number n, Quart. J. Math.48 (1917), 76-92. Zbl46.0262.03JFM46.0262.03
  9. [HM] A. Hildebrand and H. Maier: Irregularities in the distribution of primes in short intervals, J. Reine Angew. Math.397 (1989), 162-193. Zbl0658.10048MR993220
  10. [Ma] H. Maier: Primes in short intervals, Michigan Math. J.32 (1985), 221-225. Zbl0569.10023MR783576
  11. [Mo] H.L. Montgomery: Topics in Multiplicative Number Theory, Lecture Notes in Mathematics, Vol. 227, Springer-Verlag, Berlin (1971). Zbl0216.03501MR337847
  12. [Se] A. Selberg: On the normal density of primes in small intervals and the difference between consecutive primes, Arch. Math. Naturvid.47 (1943), 87-105. Zbl0063.06869MR12624

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