Comparing the number of abelian groups and of semisimple rings of a given order

Manfred Kühleitner

Displaying similar documents to “Comparing the number of abelian groups and of semisimple rings of a given order”

On a method of Balasubramanian and Ramachandra (on the abelian group problem)

A. Sankaranarayanan, K. Srinivas (1997)

Rendiconti del Seminario Matematico della Università di Padova

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Divisor problems in special sets of positive integers.

Nowak, W.G. (1992)

Acta Mathematica Universitatis Comenianae. New Series

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On the number of Abelian groups of a given order

B Srinivasan (1973)

Acta Arithmetica

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On certain arithmetic functions involving the greatest common divisor

Ekkehard Krätzel, Werner Nowak, László Tóth (2012)

Open Mathematics

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The paper deals with asymptotics for a class of arithmetic functions which describe the value distribution of the greatest-common-divisor function. Typically, they are generated by a Dirichlet series whose analytic behavior is determined by the factor ζ2(s)ζ(2s − 1). Furthermore, multivariate generalizations are considered.

On the density of the zeros of the Dedekind Zeta-function

D. Heath-Brown (1977)

Acta Arithmetica

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On the value distribution of a class of arithmetic functions

Werner Georg Nowak (1996)

Commentationes Mathematicae Universitatis Carolinae

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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 ( $N \geq 2$ a fixed integer), $α (n) > 1$ else, and $α (2^{n}) \to \infty$ . 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.