On positive sequences of reals whose block sequence has an asymptotic distribution function

József Bukor, Ferdinánd Filip and János T. Tóth
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 30, 2024, Number 3, Pages 538–546
DOI: 10.7546/nntdm.2024.30.3.538-546
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Authors and affiliations

József Bukor
Department of Informatics, J. Selye University
945 01 Komárno, Slovakia

Ferdinánd Filip
Department of Mathematics, J. Selye University
945 01 Komárno, Slovakia

János T. Tóth
Department of Mathematics, J. Selye University
945 01 Komárno, Slovakia

Abstract

In this paper we study the properties of the unbounded sequence 0 < y_1 \le y_2 \le y_3 \le \cdots of positive reals having asymptotic distribution function of the form x^\lambda. As a consequence, we immediately get information on the asymptotic behavior of the power means of order r>0 of function values of some arithmetic functions, e.g., the first n prime numbers or the values of the prime counting function.

Keywords

  • Block sequences
  • Asymptotic distribution function
  • Power mean

2020 Mathematics Subject Classification

  • 11B05
  • 11N37

References

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Manuscript history

  • Received: 18 March 2024
  • Revised: 26 September 2024
  • Accepted: 1 October 2024
  • Online First: 1 October 2024

Copyright information

Ⓒ 2024 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Cite this paper

Bukor, J., Filip, F., & Tóth, J. T. (2024). On positive sequences of reals whose block sequence has an asymptotic distribution function. Notes on Number Theory and Discrete Mathematics, 30(3), 538-546, DOI: 10.7546/nntdm.2024.30.3.538-546.

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