On the b -ary expansion of an algebraic number

Yann Bugeaud

Rendiconti del Seminario Matematico della Università di Padova (2007)

  • Volume: 118, page 217-233
  • ISSN: 0041-8994

How to cite


Bugeaud, Yann. "On the $b$-ary expansion of an algebraic number." Rendiconti del Seminario Matematico della Università di Padova 118 (2007): 217-233. <http://eudml.org/doc/108724>.

author = {Bugeaud, Yann},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {digits of -ary expansions; real algebraic numbers},
language = {eng},
pages = {217-233},
publisher = {Seminario Matematico of the University of Padua},
title = {On the $b$-ary expansion of an algebraic number},
url = {http://eudml.org/doc/108724},
volume = {118},
year = {2007},

AU - Bugeaud, Yann
TI - On the $b$-ary expansion of an algebraic number
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2007
PB - Seminario Matematico of the University of Padua
VL - 118
SP - 217
EP - 233
LA - eng
KW - digits of -ary expansions; real algebraic numbers
UR - http://eudml.org/doc/108724
ER -


  1. [1] B. ADAMCZEWSKI, Transcendance «à la Liouville» de certains nombres réels, C. R. Acad. Sci. Paris, 338 (2004), pp. 511-514. Zbl1046.11051MR2057021
  2. [2] B. ADAMCZEWSKI - Y. BUGEAUD, On the complexity of algebraic numbers I. Expansions in integer bases, Ann. of Math., 165 (2007), pp. 547-565. Zbl1195.11094MR2299740
  3. [3] B. ADAMCZEWSKI - Y. BUGEAUD, On the Maillet-Baker continued fractions, J. reine angew. Math., 606 (2007), pp. 105-121. Zbl1145.11054MR2337643
  4. [4] B. ADAMCZEWSKI - Y. BUGEAUD, Dynamics for b-shifts and Diophantine approximation, Ergodic Theory Dynam. Systems. To appear. Zbl1140.11035MR2371591
  5. [5] B. ADAMCZEWSKI - Y. BUGEAUD - F. LUCA, Sur la complexité des nombres algébriques, C. R. Acad. Sci. Paris, 339 (2004), pp. 11-14. Zbl1119.11019MR2075225
  6. [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. Zbl1076.11045MR2144954
  7. [7] E. BOMBIERI - W. GUBLER, Heights in Diophantine Geometry. New mathematical monographs 4, Cambridge University Press, 2006. Zbl1115.11034MR2216774
  8. [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. Zbl0664.10017MR951583
  9. [9] P. CORVAJA - U. ZANNIER, Some new applications of the subspace theorem, Compositio Math., 131 (2002), pp. 319-340. Zbl1010.11038MR1905026
  10. [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. Zbl0086.26402MR117220
  11. [11] M. CUGIANI, Sulla approssimabilità dei numeri algebrici mediante numeri razionali, Ann. Mat. Pura Appl., 48 (1959), pp. 135-145. Zbl0093.05402MR112880
  12. [12] J.-H. EVERTSE - H. P. SCHLICKEWEI, A quantitative version of the absolute subspace theorem, J. reine angew. Math., 548 (2002), pp. 21-127. Zbl1026.11060
  13. [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. Zbl0938.11035
  14. [14] K. MAHLER, Lectures on Diophantine approximation, Part 1: g-adic numbers and Roth's theorem, University of Notre Dame, Ann Arbor, 1961. Zbl0158.29903
  15. [15] A. RÉNYI, Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hung., 8 (1957), pp. 477-493. Zbl0079.08901
  16. [16] D. RIDOUT, Rational approximations to algebraic numbers, Mathematika, 4 (1957), pp. 125-131. Zbl0079.27401
  17. [17] D. RIDOUT, The p-adic generalization of the Thue-Siegel-Roth theorem, Mathematika, 5 (1958), pp. 40-48. Zbl0085.03501MR97382
  18. [18] T. RIVOAL, On the bits couting function of real numbers. Preprint available at: http://www-fourier.ujf-grenoble.fr/ rivoal/articles.html Zbl1234.11099MR2460868
  19. [19] T. SCHNEIDER, Einführung in die transzendenten Zahlen. Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957. Zbl0077.04703MR86842
  20. [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. Zbl0944.11024MR1756786

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