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Abstract:

We give an algorithm that computes an absolutely normal Liouville number. © 2015 American Mathematical Society.

Registro:

Documento: Artículo
Título:A computable absolutely normal Liouville number
Autor:Becher, V.; Heiber, P.A.; Slaman, T.A.
Filiación:Departmento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad, de Buenos Aires and Conicet, Argentina
The University of California, Berkeley, Department of Mathematics, 719 Evans Hall #3840, Berkeley, CA 94720-3840, United States
Palabras clave:Algorithms; Liouville numbers; Normal numbers
Año:2015
Volumen:84
Número:296
Página de inicio:2939
Página de fin:2952
DOI: http://dx.doi.org/10.1090/mcom/2964
Título revista:Mathematics of Computation
Título revista abreviado:Math. Comput.
ISSN:00255718
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v84_n296_p2939_Becher

Referencias:

  • Becher, V., Heiber, P.A., Slaman, T.A., A polynomial-time algorithm for computing absolutely normal numbers (2013) Inform. and Comput, 232, pp. 1-9. , MR3132518
  • Becher, V., Slaman, T.A., (2013) On the normality of numbers to different bases, , preprint, arXiv:1311.0333
  • Bluhm, C., On a theorem of Kaufman: Cantor-type construction of linear fractal Salem sets (1998) Ark. Mat, 36 (2), pp. 307-316. , MR1650442 (99i:43009)
  • Bluhm, C.E., Liouville numbers, Rajchman measures, and small Cantor sets (2000) Proc. Amer. Math. Soc, 128 (9), pp. 2637-2640. , MR1657762 (2000m:11063)
  • Borel, É., Les probabilités dénombrables et leurs applications arithmétiques (1909) Supplemento di Rendiconti del circolo matematico di Palermo, 27, pp. 247-271
  • Bugeaud, Y., Nombres de Liouville et nombres normaux (French, with English and French summaries) (2002) C. R. Math. Acad. Sci. Paris, 335 (2), pp. 117-120. , MR1920005 (2003e:11081)
  • Bugeaud, Y., (2012) Distribution Modulo One and Diophantine Approximation, 193. , Cambridge Tracts in MathematicsCambridge University Press, Cambridge, MR2953186
  • Davenport, H., Erdos, P., LeVeque, W.J., On Weyl's criterion for uniform distribution (1963) Michigan Math. J, 10, pp. 311-314. , MR0153656 (27 #3618)
  • Kuipers, L., Niederreiter, H., (2006) Uniform distribution of sequences, , Dover
  • Nandakumar, S., Vangapelli, S.K., (2012) Normality and finite-state dimension of Liouville numbers, , preprint, arXiv:1204.4104
  • Weyl, H., über die Gleichverteilung von Zahlen mod. Eins (German) (1916) Math. Ann, 77 (3), pp. 313-352. , MR1511862

Citas:

---------- APA ----------
Becher, V., Heiber, P.A. & Slaman, T.A. (2015) . A computable absolutely normal Liouville number. Mathematics of Computation, 84(296), 2939-2952.
http://dx.doi.org/10.1090/mcom/2964
---------- CHICAGO ----------
Becher, V., Heiber, P.A., Slaman, T.A. "A computable absolutely normal Liouville number" . Mathematics of Computation 84, no. 296 (2015) : 2939-2952.
http://dx.doi.org/10.1090/mcom/2964
---------- MLA ----------
Becher, V., Heiber, P.A., Slaman, T.A. "A computable absolutely normal Liouville number" . Mathematics of Computation, vol. 84, no. 296, 2015, pp. 2939-2952.
http://dx.doi.org/10.1090/mcom/2964
---------- VANCOUVER ----------
Becher, V., Heiber, P.A., Slaman, T.A. A computable absolutely normal Liouville number. Math. Comput. 2015;84(296):2939-2952.
http://dx.doi.org/10.1090/mcom/2964