On certain arithmetic functions involving the greatest common divisor

Ekkehard Krätzel; Werner Nowak; László Tóth

Open Mathematics (2012)

  • Volume: 10, Issue: 2, page 761-774
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Ekkehard Krätzel, Werner Nowak, and László Tóth. "On certain arithmetic functions involving the greatest common divisor." Open Mathematics 10.2 (2012): 761-774. <http://eudml.org/doc/269485>.

@article{EkkehardKrätzel2012,
abstract = {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.},
author = {Ekkehard Krätzel, Werner Nowak, László Tóth},
journal = {Open Mathematics},
keywords = {Arithmetic functions; Greatest common divisor; Asymptotic formulas; arithmetic functions; greatest common divisor; asymptotic formulas},
language = {eng},
number = {2},
pages = {761-774},
title = {On certain arithmetic functions involving the greatest common divisor},
url = {http://eudml.org/doc/269485},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Ekkehard Krätzel
AU - Werner Nowak
AU - László Tóth
TI - On certain arithmetic functions involving the greatest common divisor
JO - Open Mathematics
PY - 2012
VL - 10
IS - 2
SP - 761
EP - 774
AB - 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.
LA - eng
KW - Arithmetic functions; Greatest common divisor; Asymptotic formulas; arithmetic functions; greatest common divisor; asymptotic formulas
UR - http://eudml.org/doc/269485
ER -

References

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  7. [7] Ivic A., The Riemann Zeta-Function, John Wiley & Sons, New York, 1985 
  8. [8] Iwaniec H., Mozzochi C.J., On the divisor and circle problems, J. Number Theory, 1988, 29(1), 60–93 http://dx.doi.org/10.1016/0022-314X(88)90093-5 Zbl0644.10031
  9. [9] Krätzel E., Lattice Points, Math. Appl. (East European Ser.), 33, Kluwer, Dordrecht, 1988 
  10. [10] Phillips E., The zeta-function of Riemann; further developments of van der Corput’s method, Q. J. Math., 1933, 4, 209–225 http://dx.doi.org/10.1093/qmath/os-4.1.209 Zbl59.0204.01
  11. [11] Sloane N., The On-Line Encyclopedia of Integer Sequences, #A055155, http://oeis.org/A055155 Zbl1274.11001
  12. [12] Sloane N., The On-Line Encyclopedia of Integer Sequences, #A078430, http://oeis.org/A078430 Zbl1274.11001
  13. [13] Sloane N., The On-Line Encyclopedia of Integer Sequences, #A124316, http://oeis.org/A124316 Zbl1274.11001
  14. [14] Tanigawa Y., Zhai W., On the gcd-sum function, J. Integer Seq., 2008, 11(2), #08.2.3 Zbl1247.11124
  15. [15] Titchmarsh E.C., The Theory of the Riemann Zeta-Function, Clarendon Press, Oxford University Press, Oxford, 1986 Zbl0601.10026
  16. [16] Tóth L., Menon’s identity and arithmetical sums representing functions of several variables, Rend. Semin. Mat. Univ. Politec. Torino, 2011, 69(1), 97–110 Zbl1235.11011

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