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1999 | 89 | 2 | 97-122
Tytuł artykułu

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

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
89
Numer
2
Strony
97-122
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-03-10
poprawiono
1998-11-10
Twórcy
  • Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Straße, 35032 Marburg, Germany
Bibliografia
  • [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.
  • [2] Bombieri, E. and Vaaler, J.: On Siegel's Lemma, Invent. Math. 73 (1983), 11-32.
  • [3] Davenport, H. and Roth, K. F.: Rational approximations to algebraic numbers, Mathematika 2 (1955), 160-167.
  • [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.
  • [5] J.-H. Evertse, On equations in S-units and the Thue-Mahler equation, Invent. Math. 75 (1984), 561-584.
  • [6] J.-H. Evertse, An explicit version of Faltings' Product Theorem and an improvement of Roth's lemma, Acta Arith. 73 (1995), 215-248.
  • [7] J.-H. Evertse, An improvement of the quantitative Subspace theorem, Compositio Math. 101 (1996), 225-311.
  • [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.
  • [9] Faltings, G.: Diophantine approximation on abelian varieties, Ann. of Math. 133 (1991), 549-576.
  • [10] Luckhardt, H.: Herbrand-Analysen zweier Beweise des Satzes von Roth: polynomiale Anzahlschranken, J. Symbolic Logic 54 (1989), 234-263.
  • [11] Mahler, K.: Zur Approximation algebraischer Zahlen I. (Über den größten Primteiler binärer Formen), Math. Ann. 107 (1933), 691-730.
  • [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.
  • [13] Roth, K. F.: Rational approximations to algebraic numbers, Mathematika 2 (1955), 1-20.
  • [14] Schlickewei, H. P.: The quantitative Subspace Theorem for number fields, Compositio Math. 82 (1992), 245-273.
  • [15] Schmidt, W. M.: Simultaneous approximation to algebraic numbers by rationals, Acta Math. 125 (1970), 189-201.
  • [16] Schmidt, Diophantine Approximations, Lecture Notes in Math. 785, Springer, 1980.
  • [17] Schmidt, Diophantine Approximations and Diophantine Equations, Lecture Notes in Math. 1467, Springer, 1991.
  • [18] Stolarsky, K. B.: Algebraic Numbers and Diophantine Approximation, Dekker, 1974.
  • [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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Bibliografia
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bwmeta1.element.bwnjournal-article-aav89i2p97bwm
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