When the group-counting function assumes a prescribed integer value at squarefree integers frequently, but not extremely frequently

• Autorzy: Claudia A. Spiro-Silverman
• Języki publikacji: EN

Słowa kluczowe

EN

group-counting; squarefree order; lower bound

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1992
• Tom: 61
• Numer: 1
• Strony: 1-12

Daty

wydano

1992

otrzymano

1990-03-29

Twórcy

autor

Claudia A. Spiro-Silverman

• Mathematics Department, Boston College, Boston, Massachusetts 02167, U.S.A.

Bibliografia

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• [2] P. Erdős, M. R. Murty, and V. K. Murty, On the enumeration of finite groups, J. Number Theory 25 (1987), 360-378.
• [3] H. Halberstam and H.-E. Richert, Sieve Methods, London Math. Soc. Monographs 4, Academic Press, London 1974.
• [4] H. Halberstam and K. F. Roth, Sequences, Springer, New York 1983.
• [5] O. Hölder, Die Gruppen mit quadratfreier Ordnungszahl, Nach. Königl. Gessell. der Wiss. Göttingen Math.-Phys. Kl. 1895, 211-229.
• [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.
• [7] M.-G. Lu, The asymptotic formula for F₂(x), Sci. Sinica Ser. A 30 (1987), 262-278.
• [8] M. R. Murty and V. K. Murty, On the number of groups of a given order, J. Number Theory 18 (1984), 178-191.
• [9] K. K. Norton, On the number of restricted prime factors of an integer. I, Illinois J. Math. 20 (1976), 681-705.
• [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.
• [11] T. Szele, Über die endlichen Ordnungszahlen, zu denen nur eine Gruppe gehört, Comment. Math. Helv. 20 (1947), 265-267.
• [12] J. Szép, On finite groups which are necessarily commutative, Comment. Math. Helv., 223-224.