Displaying similar documents to “On certain arithmetic functions involving the greatest common divisor”

On a question of A. Schinzel: Omega estimates for a special type of arithmetic functions

Manfred Kühleitner, Werner Nowak (2013)

Open Mathematics

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The paper deals with lower bounds for the remainder term in asymptotics for a certain class of arithmetic functions. Typically, these are generated by a Dirichlet series of the form ζ 2(s)ζ(2s−1)ζ M(2s)H(s), where M is an arbitrary integer and H(s) has an Euler product which converges absolutely for R s > σ0, with some fixed σ0 < 1/2.

The gcd-sum function.

Broughan, Kevin A. (2001)

Journal of Integer Sequences [electronic only]

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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 ≥ 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.

On differences of two squares

Manfred Kühleitner, Werner Nowak (2006)

Open Mathematics

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The arithmetic function ρ(n) counts the number of ways to write a positive integer n as a difference of two squares. Its average size is described by the Dirichlet summatory function Σn≤x ρ(n), and in particular by the error term R(x) in the corresponding asymptotics. This article provides a sharp lower bound as well as two mean-square results for R(x), which illustrates the close connection between ρ(n) and the number-of-divisors function d(n).