On the number of good approximations of algebraic numbers by algebraic numbers of bounded degree

Helmut Locher

Acta Arithmetica (1999)

  • Volume: 89, Issue: 2, page 97-122
  • ISSN: 0065-1036

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Helmut Locher. "On the number of good approximations of algebraic numbers by algebraic numbers of bounded degree." Acta Arithmetica 89.2 (1999): 97-122. <http://eudml.org/doc/207264>.

@article{HelmutLocher1999,
author = {Helmut Locher},
journal = {Acta Arithmetica},
keywords = {approximation by algebraic numbers},
language = {eng},
number = {2},
pages = {97-122},
title = {On the number of good approximations of algebraic numbers by algebraic numbers of bounded degree},
url = {http://eudml.org/doc/207264},
volume = {89},
year = {1999},
}

TY - JOUR
AU - Helmut Locher
TI - On the number of good approximations of algebraic numbers by algebraic numbers of bounded degree
JO - Acta Arithmetica
PY - 1999
VL - 89
IS - 2
SP - 97
EP - 122
LA - eng
KW - approximation by algebraic numbers
UR - http://eudml.org/doc/207264
ER -

References

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  1. [1] Bombieri, E. and van der Poorten, A. J.: Some quantitative results related to Roth's Theorem, Macquarie Math. Reports, Report No. 87-0005, February 1987. Zbl0664.10017
  2. [2] Bombieri, E. and Vaaler, J.: On Siegel's Lemma, Invent. Math. 73 (1983), 11-32. Zbl0533.10030
  3. [3] Davenport, H. and Roth, K. F.: Rational approximations to algebraic numbers, Mathematika 2 (1955), 160-167. Zbl0066.29302
  4. [4] Esnault, H. and Viehweg, E.: Dyson's Lemma for polynomials in several variables (and the Theorem of Roth), Invent. Math. 78 (1984), 445-490. Zbl0545.10021
  5. [5] J.-H. Evertse, On equations in S-units and the Thue-Mahler equation, Invent. Math. 75 (1984), 561-584. Zbl0521.10015
  6. [6] J.-H. Evertse, An explicit version of Faltings' Product Theorem and an improvement of Roth's lemma, Acta Arith. 73 (1995), 215-248. Zbl0857.11034
  7. [7] J.-H. Evertse, An improvement of the quantitative Subspace theorem, Compositio Math. 101 (1996), 225-311. Zbl0856.11030
  8. [8] J.-H. Evertse, The number of algebraic numbers of given degree approximating a given algebraic number, in: Analytic Number Theory, Y. Motohashi (ed.), London Math. Soc. Lecture Notes Ser. 247, Cambridge Univ. Press, 1998, 53-83. Zbl0919.11048
  9. [9] Faltings, G.: Diophantine approximation on abelian varieties, Ann. of Math. 133 (1991), 549-576. Zbl0734.14007
  10. [10] Luckhardt, H.: Herbrand-Analysen zweier Beweise des Satzes von Roth: polynomiale Anzahlschranken, J. Symbolic Logic 54 (1989), 234-263. Zbl0669.03024
  11. [11] Mahler, K.: Zur Approximation algebraischer Zahlen I. (Über den größten Primteiler binärer Formen), Math. Ann. 107 (1933), 691-730. Zbl0006.10502
  12. [12] Mueller, J. and Schmidt, W. M.: On the number of good rational approximations to algebraic numbers, Proc. Amer. Math. Soc. 106 (1987), 859-866. Zbl0675.10023
  13. [13] Roth, K. F.: Rational approximations to algebraic numbers, Mathematika 2 (1955), 1-20. Zbl0064.28501
  14. [14] Schlickewei, H. P.: The quantitative Subspace Theorem for number fields, Compositio Math. 82 (1992), 245-273. Zbl0751.11033
  15. [15] Schmidt, W. M.: Simultaneous approximation to algebraic numbers by rationals, Acta Math. 125 (1970), 189-201. Zbl0205.06702
  16. [16] Schmidt, Diophantine Approximations, Lecture Notes in Math. 785, Springer, 1980. Zbl0432.10029
  17. [17] Schmidt, Diophantine Approximations and Diophantine Equations, Lecture Notes in Math. 1467, Springer, 1991. 
  18. [18] Stolarsky, K. B.: Algebraic Numbers and Diophantine Approximation, Dekker, 1974. Zbl0285.10022
  19. [19] Wirsing, E.: On approximations of algebraic numbers by algebraic numbers of bounded degree, in: Number Theory Institute 1969, Proc. Sympos. Pure Math. 20, Amer. Math. Soc., 1971, 213-247 

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