P 2 in short intervals
Annales de l'Institut Fourier, Tome 31 (1981) no. 4, pp. 37-56.

On démontre que l’intervalle [x,x+x 0,45 ] contient un entier ayant au plus deux facteurs premiers dès que x est un nombre réel suffisamment grand.

For any sufficiently large real number x, the interval [x,x+x 0,45 ] contains at least one integer having at most two prime factors .

@article{AIF_1981__31_4_37_0,
     author = {Iwaniec, Henryk and Laborde, M.},
     title = {$P_2$ in short intervals},
     journal = {Annales de l'Institut Fourier},
     pages = {37--56},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {31},
     number = {4},
     year = {1981},
     doi = {10.5802/aif.848},
     mrnumber = {83e:10061},
     zbl = {0472.10048},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.848/}
}
TY  - JOUR
AU  - Iwaniec, Henryk
AU  - Laborde, M.
TI  - $P_2$ in short intervals
JO  - Annales de l'Institut Fourier
PY  - 1981
SP  - 37
EP  - 56
VL  - 31
IS  - 4
PB  - Institut Fourier
PP  - Grenoble
UR  - http://archive.numdam.org/articles/10.5802/aif.848/
DO  - 10.5802/aif.848
LA  - en
ID  - AIF_1981__31_4_37_0
ER  - 
%0 Journal Article
%A Iwaniec, Henryk
%A Laborde, M.
%T $P_2$ in short intervals
%J Annales de l'Institut Fourier
%D 1981
%P 37-56
%V 31
%N 4
%I Institut Fourier
%C Grenoble
%U http://archive.numdam.org/articles/10.5802/aif.848/
%R 10.5802/aif.848
%G en
%F AIF_1981__31_4_37_0
Iwaniec, Henryk; Laborde, M. $P_2$ in short intervals. Annales de l'Institut Fourier, Tome 31 (1981) no. 4, pp. 37-56. doi : 10.5802/aif.848. http://archive.numdam.org/articles/10.5802/aif.848/

[1] A. A. Buchstab, Combinatorial strengthening of the sieve method of Eratosthenes (Russian), Uspehi Math. Nauk., 22 (1967), n° 3 (135), 199-226. | Zbl

[2] Jing-Run Chen, On the distribution of almost primes in an interval, Scientia Sinica, 18 (1975), 611-627. | MR | Zbl

[3] Jing-Run Chen, On the distribution of almost primes in an interval (II), Scientia Sinica, 22 (1979), 253-275. | MR | Zbl

[4] H. Halberstam and H.-E. Richert, Sieve Methods, London 1974. | MR | Zbl

[5] H. Halberstam, D. R. Heath-Brown and H.-E. Richert, Almost-primes in short intervals, to appear. | Zbl

[6] H. Iwaniec, A new form of the error term in the linear sieve, Acta Arith., 27 (1980), 307-320. | MR | Zbl

[7] W. B. Jurkat and H.-E. Richert, An improvement of Selberg sieve method, I, Acta Arith., 11 (1965), 217-240. | MR | Zbl

[8] M. Laborde, Les sommes trigonométriques de Chen et les poids de Buchstab en théorie du crible, Thèse de 3e cycle, Université de Paris-Sud.

[9] M. Laborde, Buchstab's sifting weights, Mathematika, 26 (1979), 250-257. | MR | Zbl

[10] R. A. Rankin, Van der Corput's method and the theory of exponent pairs, Quart. J. Oxford, (2) 6 (1955), 147-153. | MR | Zbl

[11] H.-E. Richert, Selberg's sieve with weights, Mathematika, 16 (1969), 1-22. | MR | Zbl

[12] E. C. Titchmarsh, The theory of the Riemann Zeta-Function, Oxford 1951. | MR | Zbl

Cité par Sources :