On the value distribution of a class of arithmetic functions

Werner Georg Nowak

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 1, page 117-134
  • ISSN: 0010-2628

Abstract

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This article deals with the value distribution of multiplicative prime-independent arithmetic functions ( α ( n ) ) with α ( n ) = 1 if n is N -free ( N 2 a fixed integer), α ( n ) > 1 else, and α ( 2 n ) . An asymptotic result is established with an error term probably definitive on the basis of the present knowledge about the zeros of the zeta-function. Applications to the enumerative functions of Abelian groups and of semisimple rings of given finite order are discussed.

How to cite

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Nowak, Werner Georg. "On the value distribution of a class of arithmetic functions." Commentationes Mathematicae Universitatis Carolinae 37.1 (1996): 117-134. <http://eudml.org/doc/247924>.

@article{Nowak1996,
abstract = {This article deals with the value distribution of multiplicative prime-independent arithmetic functions $(\alpha (n))$ with $\alpha (n)=1$ if $n$ is $N$-free ($N\ge 2$ a fixed integer), $\alpha (n)>1$ else, and $\alpha (2^n)\rightarrow \infty $. An asymptotic result is established with an error term probably definitive on the basis of the present knowledge about the zeros of the zeta-function. Applications to the enumerative functions of Abelian groups and of semisimple rings of given finite order are discussed.},
author = {Nowak, Werner Georg},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {arithmetic functions; value distribution; finite Abelian groups; asymptotic formula; multiplicative prime-independent arithmetic function; value distribution},
language = {eng},
number = {1},
pages = {117-134},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the value distribution of a class of arithmetic functions},
url = {http://eudml.org/doc/247924},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Nowak, Werner Georg
TI - On the value distribution of a class of arithmetic functions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 1
SP - 117
EP - 134
AB - This article deals with the value distribution of multiplicative prime-independent arithmetic functions $(\alpha (n))$ with $\alpha (n)=1$ if $n$ is $N$-free ($N\ge 2$ a fixed integer), $\alpha (n)>1$ else, and $\alpha (2^n)\rightarrow \infty $. An asymptotic result is established with an error term probably definitive on the basis of the present knowledge about the zeros of the zeta-function. Applications to the enumerative functions of Abelian groups and of semisimple rings of given finite order are discussed.
LA - eng
KW - arithmetic functions; value distribution; finite Abelian groups; asymptotic formula; multiplicative prime-independent arithmetic function; value distribution
UR - http://eudml.org/doc/247924
ER -

References

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  10. Nowak W.G., On the average number of finite Abelian groups of a given order, Ann. sc. math. Québec 15 (1991), 193-202. (1991) Zbl0749.11043MR1151477
  11. Rieger G.J., Zum Teilerproblem von Atle Selberg, Math. Nachr. 30 (1965), 181-192. (1965) MR0190105
  12. Selberg A., Note on a paper by L.G. Sathe, J. Indian Math. Soc. 18 (1954), 83-87. (1954) Zbl0057.28502MR0067143
  13. Wolke D., Über die zahlentheoretische Funktion ø m e g a ( n ) , Acta Arith. 55 (1990), 323-331. (1990) Zbl0705.11051MR1069186
  14. Wolke D., On a problem of A. Rényi, Monatsh. Math. 111 (1991), 323-330. (1991) Zbl0742.11045MR1116950
  15. Wu J., Sur un probléme de Rényi, Monatsh. Math. 117 (1994), 303-322. (1994) Zbl0818.11037MR1279119

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