On the b-ary expansion of an algebraic number
Bugeaud, Yann
Rendiconti del Seminario Matematico della Università di Padova, Tome 117 (2007), p. 217-233 / Harvested from Numdam
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Publié le : 2007-01-01
@article{RSMUP_2007__118__217_0,
     author = {Bugeaud, Yann},
     title = {On the $b$-ary expansion of an algebraic number},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {117},
     year = {2007},
     pages = {217-233},
     mrnumber = {2378397},
     zbl = {1174.11007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_2007__118__217_0}
}

Bugeaud, Yann. On the $b$-ary expansion of an algebraic number. Rendiconti del Seminario Matematico della Università di Padova, Tome 117 (2007) pp. 217-233. http://gdmltest.u-ga.fr/item/RSMUP_2007__118__217_0/

[1] B. Adamczewski, Transcendance «à la Liouville» de certains nombres réels, C. R. Acad. Sci. Paris, 338 (2004), pp. 511-514. | MR 2057021 | Zbl 1046.11051

[2] B. Adamczewski - Y. Bugeaud, On the complexity of algebraic numbers I. Expansions in integer bases, Ann. of Math., 165 (2007), pp. 547-565. | MR 2299740 | Zbl pre05180742

[3] B. Adamczewski - Y. Bugeaud, On the Maillet-Baker continued fractions, J. reine angew. Math., 606 (2007), pp. 105-121. | MR 2337643 | Zbl 1145.11054

[4] B. Adamczewski - Y. Bugeaud, Dynamics for b-shifts and Diophantine approximation, Ergodic Theory Dynam. Systems. To appear. | MR 2371591 | Zbl 1140.11035

[5] B. Adamczewski - Y. Bugeaud - F. Luca, Sur la complexité des nombres algébriques, C. R. Acad. Sci. Paris, 339 (2004), pp. 11-14. | MR 2075225 | Zbl 1119.11019

[6] D. H. Bailey - J. M. Borwein - R. E. Crandall - C. Pomerance, On the binary expansions of algebraic numbers, J. Théor. Nombres Bordeaux, 16 (2004), pp. 487-518. | Numdam | MR 2144954 | Zbl 1076.11045

[7] E. Bombieri - W. Gubler, Heights in Diophantine Geometry. New mathematical monographs 4, Cambridge University Press, 2006. | MR 2216774 | Zbl 1115.11034

[8] E. Bombieri - A. J. Van Der Poorten, Some quantitative results related to Roth's theorem, J. Austral. Math. Soc. Ser. A, 45 (1988), pp. 233-248. | MR 951583 | Zbl 0664.10017

[9] P. Corvaja - U. Zannier, Some new applications of the subspace theorem, Compositio Math., 131 (2002), pp. 319-340. | MR 1905026 | Zbl 1010.11038

[10] M. Cugiani, Sull'approssimabilità di un numero algebrico mediante numeri algebrici di un corpo assegnato, Boll. Un. Mat. Ital., 14 (1959), pp. 151-162. | MR 117220 | Zbl 0086.26402

[11] M. Cugiani, Sulla approssimabilità dei numeri algebrici mediante numeri razionali, Ann. Mat. Pura Appl., 48 (1959), pp. 135-145. | MR 112880 | Zbl 0093.05402

[12] J.-H. Evertse - H. P. Schlickewei, A quantitative version of the absolute subspace theorem, J. reine angew. Math., 548 (2002), pp. 21-127. | Zbl 1026.11060

[13] H. Locher, On the number of good approximations of algebraic numbers by algebraic numbers of bounded degree, Acta Arith., 89 (1999), pp. 97-122. | Zbl 0938.11035

[14] K. Mahler, Lectures on Diophantine approximation, Part 1: g-adic numbers and Roth's theorem, University of Notre Dame, Ann Arbor, 1961. | Zbl 0158.29903

[15] A. Rényi, Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hung., 8 (1957), pp. 477-493. | Zbl 0079.08901

[16] D. Ridout, Rational approximations to algebraic numbers, Mathematika, 4 (1957), pp. 125-131. | Zbl 0079.27401

[17] D. Ridout, The p-adic generalization of the Thue-Siegel-Roth theorem, Mathematika, 5 (1958), pp. 40-48. | MR 97382 | Zbl 0085.03501

[18] T. Rivoal, On the bits couting function of real numbers. Preprint available at: http://www-fourier.ujf-grenoble.fr/ rivoal/articles.html | MR 2460868

[19] T. Schneider, Einführung in die transzendenten Zahlen. Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957. | MR 86842 | Zbl 0077.04703

[20] M. Waldschmidt, Diophantine Approximation on Linear Algebraic Groups. Transcendence properties of the exponential function in several variables. Grundlehren der Mathematischen Wissenschaften 326. Springer-Verlag, Berlin, 2000. | MR 1756786 | Zbl 0944.11024