Startseite Asymptotic behavior of functions Ω(k; n) and ω(k; n) related to the number of prime divisors
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Asymptotic behavior of functions Ω(k; n) and ω(k; n) related to the number of prime divisors

  • Andrei V. Shubin EMAIL logo
Veröffentlicht/Copyright: 12. April 2019
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Abstract

This article is related to the average estimates of numerical functions Ω(k; n) and ω(k; n) connected with the number of prime divisors of n with limited multiplicity.


Note: Originally published in Diskretnaya Matematika (2017) 29, №3, 133–143 (in Russian).


References

[1] Fedorov G.V., “On the number of prime divisors of an integer with multiplicity restriction”, Izv. Saratovskogo un-ta. Novaya seriya. Ser. Matem. Mekh. Inform., 13:4 (2013), 129–133 (in Russian).10.18500/1816-9791-2013-13-4-129-133Suche in Google Scholar

[2] Naslund E., “The median largest prime factor”, J. Number Theory, 141 (2014), 109–118.10.1016/j.jnt.2013.12.018Suche in Google Scholar

[3] Shubin A. V., “Fractional parts of the function x/n”, Math. Notes, 100:5 (2016), 731–742.10.1134/S0001434616110109Suche in Google Scholar

[4] Karatsuba A. A., Principles of analytic number theory. 2nd issue, M.: Nauka, 1983 (in Russian), 240 pp.Suche in Google Scholar

[5] Gritsenko S. A., “On a density theorem”, Proc. Steklov Inst. Math., 207 (1995), 67–76.10.1007/BF01263297Suche in Google Scholar

[6] Karatsuba A. A., Voronin S. M., The Riemann zeta-function, 5, Walter de Gruyter, 1992, 396 pp.10.1515/9783110886146Suche in Google Scholar

[7] Prachar K., Primzahlverteilung, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957.Suche in Google Scholar

Received: 2016-07-24
Published Online: 2019-04-12
Published in Print: 2019-04-24

© 2019 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 30.11.2025 von https://www.degruyterbrill.com/document/doi/10.1515/dma-2019-0011/pdf
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