Geodesic
Arithmetic progressions, prime numbers, and squarefree integers
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 4, pp. 915-927
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper we establish the distribution of prime numbers in a given arithmetic progression $p \equiv l \hspace{4.44443pt}(\@mod \; k)$ for which $ap + b$ is squarefree.
In this paper we establish the distribution of prime numbers in a given arithmetic progression $p \equiv l \hspace{4.44443pt}(\@mod \; k)$ for which $ap + b$ is squarefree.
Classification : 11B05, 11B25, 11K65, 11N13, 11N25, 11N37, 11N69
Keywords: primes in arithmetic progressions; squarefree integers; Artin’s constant 
@article{CMJ_2004_54_4_a7,
     author = {Clary, Stuart and Fabrykowski, Jacek},
     title = {Arithmetic progressions, prime numbers, and squarefree integers},
     journal = {Czechoslovak Mathematical Journal},
     pages = {915--927},
     year = {2004},
     volume = {54},
     number = {4},
     mrnumber = {2100004},
     zbl = {1080.11012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2004_54_4_a7/}
}
TY  - JOUR
AU  - Clary, Stuart
AU  - Fabrykowski, Jacek
TI  - Arithmetic progressions, prime numbers, and squarefree integers
JO  - Czechoslovak Mathematical Journal
PY  - 2004
SP  - 915
EP  - 927
VL  - 54
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/CMJ_2004_54_4_a7/
LA  - en
ID  - CMJ_2004_54_4_a7
ER  - 
%0 Journal Article
%A Clary, Stuart
%A Fabrykowski, Jacek
%T Arithmetic progressions, prime numbers, and squarefree integers
%J Czechoslovak Mathematical Journal
%D 2004
%P 915-927
%V 54
%N 4
%U http://geodesic.mathdoc.fr/item/CMJ_2004_54_4_a7/
%G en
%F CMJ_2004_54_4_a7
Clary, Stuart; Fabrykowski, Jacek. Arithmetic progressions, prime numbers, and squarefree integers. Czechoslovak Mathematical Journal, Tome 54 (2004) no. 4, pp. 915-927. http://geodesic.mathdoc.fr/item/CMJ_2004_54_4_a7/

[1] Tom M. Apostol: Introduction to Analytic Number Theory. Springer-Verlag, 1976. | MR

[2] William  Ellison and Fern Ellison: Prime Numbers. John Wiley & Sons, 1985. | MR

[3] Ronald L. Graham, Donald E.  Knuth and Oren Patashnik: Concrete Mathematics: A Foundation for Computer Science. Addison-Wesley, second edition, 1994. | MR

[4] G. H. Hardy and E. M. Wright: An Introduction to the Theory of Numbers. Oxford at the Clarendon Press, fourth edition, 1960.

[5] Edmund Landau and Paul T.  Bateman: Handbuch der Lehre von der Verteilung der Primzahlen. Chelsea, New York, second edition, 1974.

[6] N. S. Mendelsohn: Private communication to Jacek Fabrykowski. 1989.

[7] L. Mirsky: The number of representations of an integer as the sum of a prime and a $k$-free integer. Amer. Math. Monthly 56 (1949), 17–19. | DOI | MR | Zbl

[8] Karl Prachar: Über die kleinste quadratfrei Zahl einer arithmetischen Reihe. Monatsh. Math. 3 (1958), 173–176. | MR

[9] John W. Wrench, Jr.: Evaluation of Artin’s constant and the twin-prime constant. Math. Comp. 15 (1961), 396–398. | MR