Accès libre

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

  
24 févr. 2025
À propos de cet article

Citez
Télécharger la couverture

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. Search in Google Scholar

HARMAN, G.: Prime-detecting Sieves. London Mathematical Society Monographs Series, Vol. 33. Princeton University Press, Princeton, NJ, 2007. Search in Google Scholar

IWANIEC, H.—KOWALSKI, E.: Analytic Number Theory. American Mathematical Society Colloquium Publications, Vol. 53. American Mathematical Society, Providence, RI, 2004. Search in Google Scholar

KUIPERS, L.—NIEDERREITER, H.: Uniform Distribution of Sequences.In: Pure and Appl. Math. Wiley-Interscience, New York-London-Sydney, 1974. Search in Google Scholar

MONTGOMERY, H. L. — VAUGHAN, R. C.: Multiplicative Number Theory I : Classical Theory. Cambridge Studies in Advanced Mathematics 97, Camebridge University Press, 2007. Search in Google Scholar

OEIS FOUNDATION INC. (2023):, The On-Line Encyclopedia of Integer Sequences. 2023 Published electronically at: http://oeis.org Search in Google Scholar

POLYMATH, D. H. J.: New equidistribution estimates of Zhang type, Algebra Number Theory 8 (2014), no. 9, 2067–2199. Search in Google Scholar

POMERANCE, C.—WEINGARTNER, A.: On primes and practical numbers, Ramanujan J. 57 (2022), no. 3, 981–1000. Search in Google Scholar

STEF, A.—TENENBAUM, G.: Entiers lexicographiques, Ramanujan J. 2 (1998), no. 1–2, 167–184. Search in Google Scholar

VAUGHAN, R. C.: On the distribution of αp modulo 1,Mathematika 24 (1977), no. 2, 135–141. Search in Google Scholar

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. Search in Google Scholar

WEINGARTNER, A.: A sieve problem and its application,Mathematika 63 (2017), no. 1, 213–229. Search in Google Scholar

WEINGARTNER, A.: An extension of the Siegel-Walfisz theorem, Proc. Amer. Math. Soc. 149 (2021), no. 11, 4699–4708. Search in Google Scholar

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 Search in Google Scholar

WEISSTEIN, E. W.: Irrationality Measure, From MathWorld—A Wolfram Web Resource; https://mathworld.wolfram.com/IrrationalityMeasure.html Search in Google Scholar