Download PDF - On the number of good approximations of algebraic numbers by algebraic numbers of bounded degreeAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

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

Authors 1

Affiliations

  1. Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Straße, 35032 Marburg, Germany

Bibliography

  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
Acta Arithmetica
1999/89/2
Export to PBN, Opens in new tab
Pages:
97-122
Main language of publication
English
Received
1998-03-10
Accepted
1998-11-10
Published
1999
Exact and natural sciences