Distinct gaps between fractional parts of sequences
HTML articles powered by AMS MathViewer
- by Marian Vâjâitu and Alexandru Zaharescu
- Proc. Amer. Math. Soc. 130 (2002), 3447-3452
- DOI: https://doi.org/10.1090/S0002-9939-02-06791-6
- Published electronically: July 15, 2002
- PDF | Request permission
Abstract:
Let $\alpha$ be a real number, $N$ a positive integer and $\mathcal N$ a subset of $\{0,1,2,\dots ,N\}$. We give an upper bound for the number of distinct lengths of gaps between the fractional parts $\{ n\alpha \},\;n\in \mathcal N$.References
- R. C. Baker, Diophantine inequalities, London Mathematical Society Monographs. New Series, vol. 1, The Clarendon Press, Oxford University Press, New York, 1986. Oxford Science Publications. MR 865981
- Florin P. Boca and Alexandru Zaharescu, Pair correlation of values of rational functions (mod $p$), Duke Math. J. 105 (2000), no. 2, 267–307. MR 1793613, DOI 10.1215/S0012-7094-00-10524-8
- Jens Marklof, The $n$-point correlations between values of a linear form, Ergodic Theory Dynam. Systems 20 (2000), no. 4, 1127–1172. With an appendix by Zeév Rudnick. MR 1779397, DOI 10.1017/S0143385700000626
- Tony van Ravenstein, The three gap theorem (Steinhaus conjecture), J. Austral. Math. Soc. Ser. A 45 (1988), no. 3, 360–370. MR 957201
- Zeév Rudnick and Peter Sarnak, The pair correlation function of fractional parts of polynomials, Comm. Math. Phys. 194 (1998), no. 1, 61–70. MR 1628282, DOI 10.1007/s002200050348
- Zeév Rudnick, Peter Sarnak, and Alexandru Zaharescu, The distribution of spacings between the fractional parts of $n^2\alpha$, Invent. Math. 145 (2001), no. 1, 37–57. MR 1839285, DOI 10.1007/s002220100141
- Zeév Rudnick and Alexandru Zaharescu, A metric result on the pair correlation of fractional parts of sequences, Acta Arith. 89 (1999), no. 3, 283–293. MR 1691857, DOI 10.4064/aa-89-3-283-293
- Wolfgang M. Schmidt, Small fractional parts of polynomials, Regional Conference Series in Mathematics, No. 32, American Mathematical Society, Providence, R.I., 1977. MR 0457360
- SÓS, V. T., On the distribution $\mod 1$ of the sequence n$\alpha ,$ Ann. Univ. Sci. Budapest, Eötvös Sect. Math. 1 (1958), 127–134.
- S. Świerczkowski, On successive settings of an arc on the circumference of a circle, Fund. Math. 46 (1959), 187–189. MR 104651, DOI 10.4064/fm-46-2-187-189
- WEYL, H., Uber die Gleichverteilung von Zahlen mod. Eins. Math. Ann. 77 (1916 ), 313-352.
Bibliographic Information
- Marian Vâjâitu
- Affiliation: Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest 70700, Romania
- Email: mvajaitu@stoilow.imar.ro
- Alexandru Zaharescu
- Affiliation: Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest 70700, Romania – and – Department of Mathematics, University of Illinois at Urbana-Champaign, Altgeld Hall, 1409 W. Green Street, Urbana, Illinois 61801
- MR Author ID: 186235
- Email: zaharesc@math.uiuc.edu
- Received by editor(s): February 7, 2001
- Published electronically: July 15, 2002
- Communicated by: David E. Rohrlich
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 3447-3452
- MSC (2000): Primary 11K06, 11B05
- DOI: https://doi.org/10.1090/S0002-9939-02-06791-6
- MathSciNet review: 1918819