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Uniform Distribution of αn Modulo One for A family of Integer Sequences Cover

Uniform Distribution of αn Modulo One for A family of Integer Sequences

Open Access
|Feb 2025

References

  1. DE BRUIJN, N. G.: On the number of positive integers ≤ x and free prime factors >y. II. Nederl. Akad. Wetensch. Proc. Ser. A 69. Indag. Math. 28 (1966) 239–247.
  2. HARMAN, G.: Prime-detecting Sieves. London Mathematical Society Monographs Series, Vol. 33. Princeton University Press, Princeton, NJ, 2007.
  3. IWANIEC, H.—KOWALSKI, E.: Analytic Number Theory. American Mathematical Society Colloquium Publications, Vol. 53. American Mathematical Society, Providence, RI, 2004.
  4. KUIPERS, L.—NIEDERREITER, H.: Uniform Distribution of Sequences.In: Pure and Appl. Math. Wiley-Interscience, New York-London-Sydney, 1974.
  5. MONTGOMERY, H. L. — VAUGHAN, R. C.: Multiplicative Number Theory I : Classical Theory. Cambridge Studies in Advanced Mathematics 97, Camebridge University Press, 2007.
  6. OEIS FOUNDATION INC. (2023):, The On-Line Encyclopedia of Integer Sequences. 2023 Published electronically at: http://oeis.org
  7. POLYMATH, D. H. J.: New equidistribution estimates of Zhang type, Algebra Number Theory 8 (2014), no. 9, 2067–2199.
  8. POMERANCE, C.—WEINGARTNER, A.: On primes and practical numbers, Ramanujan J. 57 (2022), no. 3, 981–1000.
  9. STEF, A.—TENENBAUM, G.: Entiers lexicographiques, Ramanujan J. 2 (1998), no. 1–2, 167–184.
  10. VAUGHAN, R. C.: On the distribution of αp modulo 1,Mathematika 24 (1977), no. 2, 135–141.
  11. VINOGRADOV, I. M.: The Method of Trigonometrical Sums in the Theory of Numbers. (Translated from Russian, revised and annotated by K. F. Roth and Anne Davenport), Interscience Publishers, London and New York, 1954.
  12. WEINGARTNER, A.: A sieve problem and its application,Mathematika 63 (2017), no. 1, 213–229.
  13. WEINGARTNER, A.: An extension of the Siegel-Walfisz theorem, Proc. Amer. Math. Soc. 149 (2021), no. 11, 4699–4708.
  14. WEINGARTNER, A.: The mean number of divisors for rough, dense and practical numbers, to appear in Int. J. Number Theory, arXiv:2104.07137 [math.NT] https://doi.org/10.48550/arXiv.2104.07137
  15. WEISSTEIN, E. W.: Irrationality Measure, From MathWorld—A Wolfram Web Resource; https://mathworld.wolfram.com/IrrationalityMeasure.html
DOI: https://doi.org/10.2478/udt-2023-0011 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X
Language: English
Page range: 19 - 30
Submitted on: Mar 28, 2023
Accepted on: Jun 30, 2023
Published on: Feb 24, 2025
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2025 Andreas Weingartner, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.