On the binary expansion of irrational algebraic numbers

Tanguy Rivoal[1]

  • [1] T. Rivoal, Institut Fourier, CNRS UMR 5582, Université Grenoble 1, 100 rue des Maths, BP 74, 38402 Saint-Martin d’Hères cedex, France.

Actes des rencontres du CIRM (2009)

  • Volume: 1, Issue: 1, page 55-60
  • ISSN: 2105-0597

How to cite

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Rivoal, Tanguy. "On the binary expansion of irrational algebraic numbers." Actes des rencontres du CIRM 1.1 (2009): 55-60. <http://eudml.org/doc/10019>.

@article{Rivoal2009,
affiliation = {T. Rivoal, Institut Fourier, CNRS UMR 5582, Université Grenoble 1, 100 rue des Maths, BP 74, 38402 Saint-Martin d’Hères cedex, France.},
author = {Rivoal, Tanguy},
journal = {Actes des rencontres du CIRM},
keywords = {Binary expansions; algebraic numbers; diophantine approximation; Hermite Padé approximants; Lerch function; polylogarithms; Riemann zeta function; Hurwitz zeta functions},
language = {eng},
month = {3},
number = {1},
pages = {55-60},
publisher = {CIRM},
title = {On the binary expansion of irrational algebraic numbers},
url = {http://eudml.org/doc/10019},
volume = {1},
year = {2009},
}

TY - JOUR
AU - Rivoal, Tanguy
TI - On the binary expansion of irrational algebraic numbers
JO - Actes des rencontres du CIRM
DA - 2009/3//
PB - CIRM
VL - 1
IS - 1
SP - 55
EP - 60
LA - eng
KW - Binary expansions; algebraic numbers; diophantine approximation; Hermite Padé approximants; Lerch function; polylogarithms; Riemann zeta function; Hurwitz zeta functions
UR - http://eudml.org/doc/10019
ER -

References

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  1. B. Adamczewski and Y. Bugeaud, On the complexity of algebraic numbers. I. Expansions in integer bases, Ann. of Math. (2) 165 (2007), no. 2, 547–565. Zbl1195.11094MR2299740
  2. B. Adamczewski, The many faces of ∑ n ≥ 0 2 - 2 n , slides of a talk given at the conference “Diophantine Approximation and related topics” (Tokyo) in march 2009. 
  3. D. H. Bailey, J. M. Borwein, R. E. Crandall and C. Pomerance, On the binary expansions of algebraic numbers, J. Théor. Nombres Bordeaux 16(3) (2004), 487–518. Zbl1076.11045MR2144954
  4. E. Borel, Sur les probabilités dénombrables et leurs applications arithmétiques, Rend. Circ. Mat. Palermo 27 (1909), 247–271. Zbl40.0283.01
  5. D. G. Champernowne, The construction of decimals normal in the scale of ten, J. Lond. Math. Soc bf 8 (1933), 254–260. Zbl0007.33701
  6. A. J. Kempner, On transcendental numbers, Trans. Amer. Math. Soc. 17 (1916), 476–482. Zbl46.0278.04MR1501054
  7. M.J. Knight, An “oceans of zeros” proof that a certain non-Liouville number is transcendental, Amer. Math. Monthly 98 (1991), no. 10, 947–949. Zbl0743.11034MR1137543
  8. D. Ridout, Rational approximations to algebraic numbers, Mathematika 4 (1957), 125–131. Zbl0079.27401MR93508
  9. T. Rivoal, On the bits counting function of real numbers, J. Aust. Math. Soc. 85 (2008), no. 1, 95–111. Zbl1234.11099MR2460868
  10. T. Rivoal, Convergents and irrationality measures of logarithms, Rev. Mat. Iberoamericana 23.3 (2007), 931–952. Zbl1227.11086MR2414498
  11. K. F. Roth, Rational approximations to algebraic numbers, Mathematika 2 (1955), 1–20; corrigendum, 168. Zbl0064.28501MR72182
  12. W. Sierpiński, Démonstration élémentaire du théorème de M. Borel sur les nombres absolument normaux et détermination effective d’une tel nombre, Bull. SMF 45 (1917), 125–132. Zbl46.0276.02MR1504764

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