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Approximations to the logarithms of certain rational numbers

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Pi: A Source Book

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Abstract

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.

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References

  1. A. Baker, Rational approximations to certain algebraic numbers, Proc. Lond. Math. Soc. (3)14(1964), pp. 385–398.

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  2. N. I. Feldman, Approximation by algebraic, numbers to the logarithms of algebraic numbers, Izw. Akad. Nauk. SSSK. ser. mat. 24 (1960), pp. 475–492 (in Russian).

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Authors and Affiliations

  1. Cambridge, UK

    A. Baker

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  1. A. Baker
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© 2004 Springer Science+Business Media New York

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Baker, A. (2004). Approximations to the logarithms of certain rational numbers. In: Pi: A Source Book. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4217-6_40

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  • DOI: https://doi.org/10.1007/978-1-4757-4217-6_40

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-1915-1

  • Online ISBN: 978-1-4757-4217-6

  • eBook Packages: Springer Book Archive

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