Effective measures of irrationality for cubic extensions of number fields

E. Bombieri; A. J. Van der Poorten; J. D. Vaaler

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1996)

  • Volume: 23, Issue: 2, page 211-248
  • ISSN: 0391-173X

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Bombieri, E., Van der Poorten, A. J., and Vaaler, J. D.. "Effective measures of irrationality for cubic extensions of number fields." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 23.2 (1996): 211-248. <http://eudml.org/doc/84230>.

@article{Bombieri1996,
author = {Bombieri, E., Van der Poorten, A. J., Vaaler, J. D.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {effective diophantine approximation; cubic extensions; effective irrationality measure},
language = {eng},
number = {2},
pages = {211-248},
publisher = {Scuola normale superiore},
title = {Effective measures of irrationality for cubic extensions of number fields},
url = {http://eudml.org/doc/84230},
volume = {23},
year = {1996},
}

TY - JOUR
AU - Bombieri, E.
AU - Van der Poorten, A. J.
AU - Vaaler, J. D.
TI - Effective measures of irrationality for cubic extensions of number fields
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1996
PB - Scuola normale superiore
VL - 23
IS - 2
SP - 211
EP - 248
LA - eng
KW - effective diophantine approximation; cubic extensions; effective irrationality measure
UR - http://eudml.org/doc/84230
ER -

References

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  2. [2] A. Baker, Simultaneous rational approximations to certain algebraic numbers, Proc. Camb. Phil. Soc.63 (1967), 693-702. Zbl0166.05503MR213303
  3. [3] A. Baker, Linear forms in the logarithms of algebraic numbers I, II, III, IV, Mathematika13 (1966), 204-16; 14 (1967), 102-107, 220-228; 15 (1968), 204-216. MR220680
  4. [4] A. Baker - C.L. Stewart, On effective approximations to cubic irrationals, New Advances in Transcendence Theorey, A. Baker, ed., Cambridge University Press, 1988, 1-24. Zbl0656.10025MR971990
  5. [5] E. Bombieri, On the Thue-Siegel-Dyson Theorem, Acta Math.148 (1982), 255-296. Zbl0505.10015MR666113
  6. [6] E. Bombieri, Effective Diophantine approximation on G m, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 20 (1993), n. 1, 61-89. Zbl0774.11034MR1215999
  7. [7] E. Bombieri - J. Mueller, On effective measures of irrationality for r√a/b and related numbers, J. Reine Angew. Math.342 (1983), 173-196. Zbl0516.10024
  8. [8] E. Bombieri - J. Vaaler, On Siegel's Lemma, Invent. Math.73 (1983), 11-32. Zbl0533.10030MR707346
  9. [9] K.-K. Choi, preprint. 
  10. [10] G.V. Chudnovsky, On the method of Thue-Siegel, Ann. of Math. (2) 117 (1983), 325-382. Zbl0518.10038MR690849
  11. [11] N.I. Feldman, An effective refinement of the exponent in Liouville's theorem, (Russian), Izv. Akad. Nauk35 (1971), 973-990. Also: Math. USSR Izv.5 (1971), 985-1002. Zbl0259.10031MR289418
  12. [12] A. Néron, Modèles Minimaux des Variétés Abéliennes sur les Corps Locaux et Globaux, IHES Publications Mathématiques, n. 21, Presses Universitaires de France, 1964. Zbl0132.41403MR179172
  13. [13] C.G. Pinner - J.D. Vaaler, The Number of Irreducible Factors of a Polynomial, I, Trans. Amer. Math. Soc. (1993), 809-834. Zbl0787.11045MR1150018
  14. [14] R.S. Rumely, Capacity Theory on Algebraic Curves, Lecture Notes in Mathematics1378, Springer-Verlag, New York, 1989. Zbl0679.14012MR1009368
  15. [15] W.M. Schmidt, Simultaneous Approximation to Algebraic Numbers by Elements of a Number field, Monatsh. Math.79 (1975), 55-66. Zbl0317.10042MR364112
  16. [16] A. Thue, Über Annäherungswerte algebraischer Zahlen, J. Reine Angew. Math. 136 (1909), 284-305. JFM40.0265.01
  17. [17] S.M. Tyler, The Lagrange Spectrum in Projective Space over a Local Field, Ph.D. Dissertation, The University of Texas at Austin, 1994. 
  18. [18] P. Vojta, Dyson's lemma for products of two curves of arbitrary genus, Invent. Math.98 (1989), 107-113. Zbl0666.10024MR1010157

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