Approximations to the logarithms of certain rational numbers

  • A. Baker


In a recent paper [1] methods were introduced for investigating the accuracy with which certain algebraic numbers may be approximated by rational numbers. It is the main purpose of the present paper to deduce, using similar techniques, results concerning the accuracy with which the natural logarithms of certain rational numbers may be approximated by rational numbers, or, more generally, by algebraic numbers of bounded degree.


Positive Integer Linear Form Rational Number Algebraic Number Strong Estimate 
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  1. [1]
    A. Baker, Rational approximations to certain Loud. Math. Soc. (3)14(1904), pp. 385–398.CrossRefGoogle Scholar
  2. [2]
    N. I. Feldman, Approximation by algebraic algebraic cumbers,Izw. Akad. Nauk. SSSR. ser. mat Russian).Google Scholar
  3. [3]
    K. Mahler, Zur Approximation der Exponentiatfunktion und des,Jour. reine. angcw. Mai. h. 166 (1932), (1) pp. I18–136, (II) pp. 137–150.Google Scholar
  4. [4]
    K. Mahler, On the approximation of logarithms of algebraic numbers, Philos. Trans. Roy. Soc. Lond., ser. A, 245 (1953), pp. 371–398.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    K. Mahler, On the approximation of r, Proc. Akad. Wetensob. Amst., ser. A, 56 (1953), pp. 30–42.MathSciNetGoogle Scholar
  6. [6]
    D. Morduehai-Boltowskoj, Sur le logarithme d’un, nombre algebriquc, Comptes Rendus Acad. Sei., Paris, 176 (1923), pp. 724–727.Google Scholar
  7. [7]
    Th. Schneider, Einführung in die transzendenten Zahlen, Berlin,Giittingen, Heidelberg, 1957, Kap. 4.Google Scholar
  8. [8]
    C. L. Siegel, Über einige Anwendungen diophantischer Approximationen.,Abh. Preuss. Akad. Wiss. (1929), No 1.Google Scholar
  9. [9]
    E. Wirsing, Approximation suit algebraischen. Zahlen beschrankten. Grades. Jour. reine. angew. Math. 206 (1961), pp. 67–77.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • A. Baker
    • 1
  1. 1.CambridgeUK

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