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

Abstract

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In this paper we establish the distribution of prime numbers in a given arithmetic progression p ≡ l ( m o d k ) for which a p + b is squarefree.

How to cite

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Clary, 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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  1. Introduction to Analytic Number Theory, Springer-Verlag, 1976. (1976) MR0434929
  2. Prime Numbers, John Wiley & Sons, 1985. (1985) MR0814687
  3. Concrete Mathematics: A Foundation for Computer Science, Addison-Wesley, second edition, 1994. (1994) MR1397498
  4. An Introduction to the Theory of Numbers, Oxford at the Clarendon Press, fourth edition, 1960. (1960) 
  5. Handbuch der Lehre von der Verteilung der Primzahlen, Chelsea, New York, second edition, 1974. (1974) 
  6. Private communication to Jacek Fabrykowski, 1989. (1989) 
  7. 10.2307/2305811, Amer. Math. Monthly 56 (1949), 17–19. (1949) Zbl0033.16203MR0028335DOI10.2307/2305811
  8. Über die kleinste quadratfrei Zahl einer arithmetischen Reihe, Monatsh. Math. 3 (1958), 173–176. (1958) MR0092806
  9. Evaluation of Artin’s constant and the twin-prime constant, Math. Comp. 15 (1961), 396–398. (1961) MR0124305

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