Registro:
Documento: |
Artículo
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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
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Palabras clave: | Discrepancy; Normal numbers; Uniform distribution |
Año: | 2017
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Volumen: | 180
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Número: | 4
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Página de inicio: | 333
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Página de fin: | 346
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DOI: |
http://dx.doi.org/10.4064/aa170213-5-8 |
Título revista: | Acta Arithmetica
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Título revista abreviado: | Acta Arith.
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ISSN: | 00651036
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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