Arithmetic progressions, prime numbers, and squarefree integers
Stuart Clary; Jacek Fabrykowski
Czechoslovak Mathematical Journal (2004)
- Volume: 54, Issue: 4, page 915-927
- ISSN: 0011-4642
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topClary, Stuart, and Fabrykowski, Jacek. "Arithmetic progressions, prime numbers, and squarefree integers." Czechoslovak Mathematical Journal 54.4 (2004): 915-927. <http://eudml.org/doc/30910>.
@article{Clary2004,
abstract = {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.},
author = {Clary, Stuart, Fabrykowski, Jacek},
journal = {Czechoslovak Mathematical Journal},
keywords = {primes in arithmetic progressions; squarefree integers; Artin’s constant; primes in arithmetic progressions; squarefree integers; Artin's constant},
language = {eng},
number = {4},
pages = {915-927},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Arithmetic progressions, prime numbers, and squarefree integers},
url = {http://eudml.org/doc/30910},
volume = {54},
year = {2004},
}
TY - JOUR
AU - Clary, Stuart
AU - Fabrykowski, Jacek
TI - Arithmetic progressions, prime numbers, and squarefree integers
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 4
SP - 915
EP - 927
AB - 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.
LA - eng
KW - primes in arithmetic progressions; squarefree integers; Artin’s constant; primes in arithmetic progressions; squarefree integers; Artin's constant
UR - http://eudml.org/doc/30910
ER -
References
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- Handbuch der Lehre von der Verteilung der Primzahlen, Chelsea, New York, second edition, 1974. (1974)
- Private communication to Jacek Fabrykowski, 1989. (1989)
- 10.2307/2305811, Amer. Math. Monthly 56 (1949), 17–19. (1949) Zbl0033.16203MR0028335DOI10.2307/2305811
- Über die kleinste quadratfrei Zahl einer arithmetischen Reihe, Monatsh. Math. 3 (1958), 173–176. (1958) MR0092806
- Evaluation of Artin’s constant and the twin-prime constant, Math. Comp. 15 (1961), 396–398. (1961) MR0124305
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