# 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

## Access Full Article

top## How to cite

topFriedlander, John, and Granville, Andrew. "Limitations to the equi-distribution of primes III." Compositio Mathematica 81.1 (1992): 19-32. <http://eudml.org/doc/90130>.

@article{Friedlander1992,

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 = {http://eudml.org/doc/90130},

volume = {81},

year = {1992},

}

TY - JOUR

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 - http://eudml.org/doc/90130

ER -

## References

top- [BFI] E. Bombieri, J.B. Friedlander, and H. Iwaniec: Primes in arithmetic progressions to large moduli, Acta Math.156 (1986), 203-251II, Math. Ann.277 (1987), 361-393; III, J. Amer. Math. Soc.2 (1989), 215-224. Zbl0674.10036MR834613
- [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
- [Da] H. Davenport: Multiplicative Number Theory (2nd ed.), Springer-Verlag, New York (1980). Zbl0453.10002MR606931
- [FG] J. Friedlander and A. Granville: Limitations to the equi-distribution of primes I, Ann. Math.129 (1989), 363-382. Zbl0671.10041MR986796
- [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
- [Ga] P.X. Gallagher: A large sieve density estimate near σ = 1, Invent. Math.11 (1970), 329-339. Zbl0219.10048
- [HRi] H. Halberstam and H.-E. Richert: Sieve Methods, L.M.S. Monographs, Academic Press, London (1974). Zbl0298.10026MR424730
- [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
- [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
- [Ma] H. Maier: Primes in short intervals, Michigan Math. J.32 (1985), 221-225. Zbl0569.10023MR783576
- [Mo] H.L. Montgomery: Topics in Multiplicative Number Theory, Lecture Notes in Mathematics, Vol. 227, Springer-Verlag, Berlin (1971). Zbl0216.03501MR337847
- [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

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.