A computable absolutely normal Liouville number
HTML articles powered by AMS MathViewer
- by Verónica Becher, Pablo Ariel Heiber and Theodore A. Slaman PDF
- Math. Comp. 84 (2015), 2939-2952
Abstract:
We give an algorithm that computes an absolutely normal Liouville number.References
- Verónica Becher, Pablo Ariel Heiber, and Theodore A. Slaman, A polynomial-time algorithm for computing absolutely normal numbers, Inform. and Comput. 232 (2013), 1–9. MR 3132518, DOI 10.1016/j.ic.2013.08.013
- V. Becher and T. A. Slaman, On the normality of numbers to different bases, preprint, arXiv:1311.0333, 2013.
- Christian Bluhm, On a theorem of Kaufman: Cantor-type construction of linear fractal Salem sets, Ark. Mat. 36 (1998), no. 2, 307–316. MR 1650442, DOI 10.1007/BF02384771
- Christian E. Bluhm, Liouville numbers, Rajchman measures, and small Cantor sets, Proc. Amer. Math. Soc. 128 (2000), no. 9, 2637–2640. MR 1657762, DOI 10.1090/S0002-9939-00-05276-X
- É. Borel, Les probabilités dénombrables et leurs applications arithmétiques, Supplemento di Rendiconti del circolo matematico di Palermo, 27 1909, 247–271
- Yann Bugeaud, Nombres de Liouville et nombres normaux, C. R. Math. Acad. Sci. Paris 335 (2002), no. 2, 117–120 (French, with English and French summaries). MR 1920005, DOI 10.1016/S1631-073X(02)02456-1
- Yann Bugeaud, Distribution modulo one and Diophantine approximation, Cambridge Tracts in Mathematics, vol. 193, Cambridge University Press, Cambridge, 2012. MR 2953186, DOI 10.1017/CBO9781139017732
- H. Davenport, P. Erdős, and W. J. LeVeque, On Weyl’s criterion for uniform distribution, Michigan Math. J. 10 (1963), 311–314. MR 153656
- L. Kuipers and H. Niederreiter, Uniform distribution of sequences, Dover, 2006.
- Satyadev Nandakumar and Santhosh Kumar Vangapelli, Normality and finite-state dimension of Liouville numbers, preprint, arXiv:1204.4104, 2012.
- Hermann Weyl, Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1916), no. 3, 313–352 (German). MR 1511862, DOI 10.1007/BF01475864
Additional Information
- Verónica Becher
- Affiliation: Departmento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires & CONICET, Argentina
- MR Author ID: 368040
- Email: vbecher@dc.uba.ar
- Pablo Ariel Heiber
- Affiliation: Departmento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires & CONICET, Argentina
- Email: pheiber@dc.uba.ar
- Theodore A. Slaman
- Affiliation: The University of California, Berkeley, Department of Mathematics, 719 Evans Hall #3840, Berkeley, California 94720-3840
- MR Author ID: 163530
- Email: slaman@math.berkeley.edu
- Received by editor(s): January 29, 2014
- Received by editor(s) in revised form: April 14, 2014
- Published electronically: April 24, 2015
- Additional Notes: The first and second authors were supported by Agencia Nacional de Promoción Científica y Tecnológica and CONICET, Argentina.
The third author was partially supported by the National Science Foundation, USA, under Grant No. DMS-1001551 and by the Simons Foundation. - © Copyright 2015 By the authors
- Journal: Math. Comp. 84 (2015), 2939-2952
- MSC (2010): Primary 11K16, 68-04; Secondary 11-04
- DOI: https://doi.org/10.1090/mcom/2964
- MathSciNet review: 3378855