General -product function.
Loveless, Andrew D. (2006)
Integers
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Displaying similar documents to “The gcd-sum function.”
General -product function.
On a generalization of a formula of Sierpiński.
Kühleitner, Manfred (1998)
Mathematica Pannonica
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The average order of the Dirichlet series of the gcd-sum function.
Broughan, Kevin A. (2007)
Journal of Integer Sequences [electronic only]
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Mean values of generalized gcd-sum and lcm-sum functions.
Bordellès, Olivier (2007)
Journal of Integer Sequences [electronic only]
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Mean values of a gcd-sum function over regular integers modulo .
Zhang, Deyu, Zhai, Wenguang (2010)
Journal of Integer Sequences [electronic only]
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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.
A survey of gcd-sum functions.
Tóth, László (2010)
Journal of Integer Sequences [electronic only]
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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.
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.
Square-full divisors of square-full integers.
Ledoan, A.H., Zaharescu, A. (2010)
Integers
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Higher correlations of divisor sums related to primes. I: Triple correlations.
Goldston, D. A., Yıldırım, C. Y. (2003)
Integers
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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).