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Documento: Artículo
Título:On the construction of absolutely normal numbers
Autor:Aistleitner, C.; Becher, V.; Scheerer, A.-M.; Slaman, T.A.
Filiación:Institute of Analysis and Number Theory, Graz University of Technology, Graz, A-8010, Austria
Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, ICC, CONICET, Pabellón I, Buenos Aires, C1428EGA, Argentina
Department of Mathematics, University of California Berkeley, 719 Evans Hall #3840, Berkeley, CA 94720-3840, United States
Palabras clave:Discrepancy; Normal numbers; Uniform distribution
Año:2017
Volumen:180
Número:4
Página de inicio:333
Página de fin:346
DOI: http://dx.doi.org/10.4064/aa170213-5-8
Título revista:Acta Arithmetica
Título revista abreviado:Acta Arith.
ISSN:00651036
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00651036_v180_n4_p333_Aistleitner

Referencias:

  • Aistleitner, C., Berkes, I., Limit distributions in metric discrepancy theory (2013) Monatsh. Math., 169, pp. 253-265
  • Alvarez, N., Becher, V., Levin, M., Construction of absolutely normal numbers with very low discrepancy (2017) Math. Comp., 86, pp. 2927-2946
  • Becher, V., Heiber, P., Slaman, T., A polynomial-time algorithm for computing absolutely normal numbers (2013) Inform. and Comput., 232, pp. 1-9
  • Bugeaud, Y., (2012) Distribution Modulo One and Diophantine Approximation, , Cambridge Tracts in Math. 193, Cambridge Univ. Press, Cambridge
  • Fukuyama, K., The law of the iterated logarithm for discrepancies of {θn x} (2008) Acta Math. Hungar., 118, pp. 155-170
  • Gál, S., Gál, L., The discrepancy of the sequence {(2nx)} (1964) Nederl. Akad. Wetensch. Proc. Ser. A 67 = Indag. Math., 26, pp. 129-143
  • Korobov, N., On completely uniform distribution and jointly normal numbers (1956) Izv. Akad. Nauk SSSR Ser. Mat., 20, pp. 649-660. , (in Russian)
  • Levin, M., On absolutely normal numbers (1979) Vestnik Moskov. Univ. Ser. Mat. Mekh., 1, pp. 31-37. , (in Russian); English transl.: Moscow Univ. Math. Bull. 34 (1979), no. 1, 32-39
  • Levin, M., On the discrepancy estimate of normal numbers (1999) Acta Arith., 88, pp. 99-111
  • Philipp, W., Limit theorems for lacunary series and uniform distribution mod 1 (1975) Acta Arith., 26, pp. 241-251
  • Scheerer, A.-M., Computable absolutely normal numbers and discrepancies (2017) Math. Comput., 86, pp. 2911-2926
  • Schmidt, W., Irregularities of distribution. VII (1972) Acta Arith., 21, pp. 45-50
  • Stroock, D., (1993) Probability Theory. An Analytic View, , Cambridge Univ. Press, Cambridge
  • Van Der-Vaart, A., Wellner, J., (1996) Weak Convergence and Empirical Processes, , Springer Ser. Statist., Springer, New York

Citas:

---------- APA ----------
Aistleitner, C., Becher, V., Scheerer, A.-M. & Slaman, T.A. (2017) . On the construction of absolutely normal numbers. Acta Arithmetica, 180(4), 333-346.
http://dx.doi.org/10.4064/aa170213-5-8
---------- CHICAGO ----------
Aistleitner, C., Becher, V., Scheerer, A.-M., Slaman, T.A. "On the construction of absolutely normal numbers" . Acta Arithmetica 180, no. 4 (2017) : 333-346.
http://dx.doi.org/10.4064/aa170213-5-8
---------- MLA ----------
Aistleitner, C., Becher, V., Scheerer, A.-M., Slaman, T.A. "On the construction of absolutely normal numbers" . Acta Arithmetica, vol. 180, no. 4, 2017, pp. 333-346.
http://dx.doi.org/10.4064/aa170213-5-8
---------- VANCOUVER ----------
Aistleitner, C., Becher, V., Scheerer, A.-M., Slaman, T.A. On the construction of absolutely normal numbers. Acta Arith. 2017;180(4):333-346.
http://dx.doi.org/10.4064/aa170213-5-8