Artículo
Becher, V.; Bugeaud, Y.; Slaman, T.A. "The irrationality exponents of computable numbers" (2016) Proceedings of the American Mathematical Society. 144(4):1509-1521
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Abstract:
We establish that there exist computable real numbers whose irrationality exponent is not computable. © 2015 American Mathematical Society.
Registro:
| Documento: | Artículo |
| Título: | The irrationality exponents of computable numbers |
| Autor: | Becher, V.; Bugeaud, Y.; Slaman, T.A. |
| Filiación: | Departamento de Computacion, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Ciudad Autónoma de Buenos Aires, C1428EGA, Argentina UFR de Mathématique et d’Informatique, Université de Strasbourg, 7 rue René Descartes, Strasbourg Cedex, 67084, France Department of Mathematics, University of California Berkeley, 970 Evans Hall, Berkeley, CA 94720, United States |
| Palabras clave: | Cantor set; Computability; Irrationality exponent |
| Año: | 2016 |
| Volumen: | 144 |
| Número: | 4 |
| Página de inicio: | 1509 |
| Página de fin: | 1521 |
| DOI: | http://dx.doi.org/10.1090/proc/12841 |
| Título revista: | Proceedings of the American Mathematical Society |
| Título revista abreviado: | Proc. Am. Math. Soc. |
| ISSN: | 00029939 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v144_n4_p1509_Becher |
Referencias:
- Besicovitch, A.S., Sets of Fractional Dimensions (IV): On Rational Approximation to Real Numbers (1934) J. London Math. Soc, 2, p. 126. , MR1574327
- Bugeaud, Y., Diophantine approximation and Cantor sets (2008) Math. Ann, 341 (3), pp. 677-684. , MR2399165 (2009h:11116)
- Falconer, K., (2003) Fractal Geometry, , 2nd ed., Mathematical foundations and applications, John Wiley & Sons, Inc., Hoboken, NJ, MR2118797 (2006b:28001)
- Jarník, V., (1928) Prace Mat.-Fiz, 36, pp. 91-106. , Zur metrischen theorie der diophantischen approximation, 1929
- Vojtˇech, J., Uber die simultanen diophantischen Approximationen (German) (1931) Math. Z, 33 (1), pp. 505-543. , MR1545226
- Wolfgang, M., Schmidt, Diophantine approximation (1980) Lecture Notes in Mathematics, 785. , Springer, Berlin, MR568710 (81j:10038)
- Shallit, J.O., Simple continued fractions for some irrational numbers. II (1982) J. Number Theory, 14 (2), pp. 228-231. , MR655726 (84a:10035)
- Soare, R.I., Recursive theory and Dedekind cuts (1969) Trans. Amer. Math. Soc., 140, pp. 271-294. , MR0242667 (39 #3997)
- Robert, I., (1987) Soare, Recursively Enumerable Sets and Degrees, a Study of Computable Functions and Computably Generated Sets. Perspectives in Mathematical Logic, , Springer-Verlag, Berlin, MR882921 (88m:03003)
Citas:
---------- APA ----------
Becher, V., Bugeaud, Y. & Slaman, T.A. (2016) . The irrationality exponents of computable numbers. Proceedings of the American Mathematical Society, 144(4), 1509-1521.http://dx.doi.org/10.1090/proc/12841
---------- CHICAGO ----------
Becher, V., Bugeaud, Y., Slaman, T.A. "The irrationality exponents of computable numbers" . Proceedings of the American Mathematical Society 144, no. 4 (2016) : 1509-1521.http://dx.doi.org/10.1090/proc/12841
---------- MLA ----------
Becher, V., Bugeaud, Y., Slaman, T.A. "The irrationality exponents of computable numbers" . Proceedings of the American Mathematical Society, vol. 144, no. 4, 2016, pp. 1509-1521.http://dx.doi.org/10.1090/proc/12841
---------- VANCOUVER ----------
Becher, V., Bugeaud, Y., Slaman, T.A. The irrationality exponents of computable numbers. Proc. Am. Math. Soc. 2016;144(4):1509-1521.http://dx.doi.org/10.1090/proc/12841
