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

Manfred Kühleitner; Werner Nowak

Displaying similar documents to “On a question of A. Schinzel: Omega estimates for a special type of arithmetic functions”

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.

General $gcd$ -product function.

Loveless, Andrew D. (2006)

Integers

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Square-full divisors of square-full integers.

Ledoan, A.H., Zaharescu, A. (2010)

Integers

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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.

Upper bounds for the moments of derivatives of Dirichlet L-functions

Keiju Sono (2014)

Open Mathematics

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In this paper, we give certain upper bounds for the 2k-th moments, k ≥ 1/2, of derivatives of Dirichlet L-functions at s = 1/2 under the assumption of the Generalized Riemann Hypothesis.

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).

Mean values of generalized gcd-sum and lcm-sum functions.

Bordellès, Olivier (2007)

Journal of Integer Sequences [electronic only]

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On Hecke $L$ -functions associated with cusp forms. II: On the sign changes of $S_{f} (T)$ .

Sankaranarayanan, A. (2006)

Annales Academiae Scientiarum Fennicae. Mathematica

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Note on a Paper by h. l. Montgomery ``omega Theorems for the Riemann Zeta-function''

K. Ramachandra, A. Sankaranarayanan (1991)

Publications de l'Institut Mathématique

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Note on a Paper by h. l. Montgomery ``omega Theorems for the Riemann Zeta-function''

K. Ramachandra, A. Sankaranarayanan (1991)

Publications de l'Institut Mathématique

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Some problems on mean values of the Riemann zeta-function

Aleksandar Ivić (1996)

Journal de théorie des nombres de Bordeaux

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Several problems and results on mean values of $ζ (s)$ are discussed. These include mean values of $| ζ (\frac{1}{2} + i t) |$ and the fourth moment of $| ζ (σ + i t) |$ for $1 / 2 < σ < 1$ .