| Title:
|
Arithmetic progressions, prime numbers, and squarefree integers (English) |
| Author:
|
Clary, Stuart |
| Author:
|
Fabrykowski, Jacek |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
54 |
| Issue:
|
4 |
| Year:
|
2004 |
| Pages:
|
915-927 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
primes in arithmetic progressions |
| Keyword:
|
squarefree integers |
| Keyword:
|
Artin’s constant |
| MSC:
|
11B05 |
| MSC:
|
11B25 |
| MSC:
|
11K65 |
| MSC:
|
11N13 |
| MSC:
|
11N25 |
| MSC:
|
11N37 |
| MSC:
|
11N69 |
| idZBL:
|
Zbl 1080.11012 |
| idMR:
|
MR2100004 |
| . |
| Date available:
|
2009-09-24T11:18:52Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127940 |
| . |
| Reference:
|
[1] Tom M. Apostol: Introduction to Analytic Number Theory.Springer-Verlag, 1976. MR 0434929 |
| Reference:
|
[2] William Ellison and Fern Ellison: Prime Numbers.John Wiley & Sons, 1985. MR 0814687 |
| Reference:
|
[3] Ronald L. Graham, Donald E. Knuth and Oren Patashnik: Concrete Mathematics: A Foundation for Computer Science.Addison-Wesley, second edition, 1994. MR 1397498 |
| Reference:
|
[4] G. H. Hardy and E. M. Wright: An Introduction to the Theory of Numbers.Oxford at the Clarendon Press, fourth edition, 1960. |
| Reference:
|
[5] Edmund Landau and Paul T. Bateman: Handbuch der Lehre von der Verteilung der Primzahlen.Chelsea, New York, second edition, 1974. |
| Reference:
|
[6] N. S. Mendelsohn: Private communication to Jacek Fabrykowski.1989. |
| Reference:
|
[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. Zbl 0033.16203, MR 0028335, 10.2307/2305811 |
| Reference:
|
[8] Karl Prachar: Über die kleinste quadratfrei Zahl einer arithmetischen Reihe.Monatsh. Math. 3 (1958), 173–176. MR 0092806 |
| Reference:
|
[9] John W. Wrench, Jr.: Evaluation of Artin’s constant and the twin-prime constant.Math. Comp. 15 (1961), 396–398. MR 0124305 |
| . |
