When the group-counting function assumes a prescribed integer value at squarefree integers frequently, but not extremely frequently
Claudia A. Spiro-Silverman
Acta Arithmetica, Tome 62 (1992), p. 1-12 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)
Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:206449 
@article{bwmeta1.element.bwnjournal-article-aav61i1p1bwm,
     author = {Claudia A. Spiro-Silverman},
     title = {When the group-counting function assumes a prescribed integer value at squarefree integers frequently, but not extremely frequently},
     journal = {Acta Arithmetica},
     volume = {62},
     year = {1992},
     pages = {1-12},
     zbl = {0747.11039},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav61i1p1bwm}
}

Claudia A. Spiro-Silverman. When the group-counting function assumes a prescribed integer value at squarefree integers frequently, but not extremely frequently. Acta Arithmetica, Tome 62 (1992) pp. 1-12. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav61i1p1bwm/

[000] [1] P. Erdős, Some asymptotic formulas in number theory, J. Indian Math. Soc. 12 (1948), 75-78. | Zbl 0041.36807

[001] [2] P. Erdős, M. R. Murty, and V. K. Murty, On the enumeration of finite groups, J. Number Theory 25 (1987), 360-378. | Zbl 0612.10038

[002] [3] H. Halberstam and H.-E. Richert, Sieve Methods, London Math. Soc. Monographs 4, Academic Press, London 1974. | Zbl 0298.10026

[003] [4] H. Halberstam and K. F. Roth, Sequences, Springer, New York 1983.

[004] [5] O. Hölder, Die Gruppen mit quadratfreier Ordnungszahl, Nach. Königl. Gessell. der Wiss. Göttingen Math.-Phys. Kl. 1895, 211-229. | Zbl 26.0162.01

[005] [6] Yu. V. Linnik, On the least prime in an arithmetic progression. II. The Deuring-Heilbronn phenomenon, Mat. Sb. (N.S.) 15 (57) (1944), 347-368. | Zbl 0063.03585

[006] [7] M.-G. Lu, The asymptotic formula for F₂(x), Sci. Sinica Ser. A 30 (1987), 262-278.

[007] [8] M. R. Murty and V. K. Murty, On the number of groups of a given order, J. Number Theory 18 (1984), 178-191. | Zbl 0531.10047

[008] [9] K. K. Norton, On the number of restricted prime factors of an integer. I, Illinois J. Math. 20 (1976), 681-705. | Zbl 0329.10035

[009] [10] C. A. Spiro, The probability that the number of groups of squarefree order is two more than a fixed prime, Proc. London Math. Soc. 60 (1990), 444-470. | Zbl 0707.11066

[010] [11] T. Szele, Über die endlichen Ordnungszahlen, zu denen nur eine Gruppe gehört, Comment. Math. Helv. 20 (1947), 265-267. | Zbl 0034.30502

[011] [12] J. Szép, On finite groups which are necessarily commutative, Comment. Math. Helv., 223-224. | Zbl 0035.01502