## On the linear independence measure of logarithms of rational numbers

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## Abstract:

In this paper we give a general theorem on the linear independence measure of logarithms of rational numbers and, in particular, the linear independence measure of $1,\log 2, \log 3, \log 5$ and of $1,\log 2, \log 3, \log 5, \log 7$. We also give a method to search for polynomials of smallest norm on a real interval $[a,b]$ which may be suitable for computing or improving the linear independence measure of logarithms of rational numbers.## References

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## Additional Information

**Qiang Wu**- Affiliation: Département de Mathématique, Université de Metz, Ile du Saulcy, 57045 Metz Cedex 1, France
- Email: wu@poncelet.univ-metz.fr
- Received by editor(s): April 17, 2001
- Received by editor(s) in revised form: September 5, 2001
- Published electronically: June 25, 2002
- © Copyright 2002 American Mathematical Society
- Journal: Math. Comp.
**72**(2003), 901-911 - MSC (2000): Primary 11J82, 11J86
- DOI: https://doi.org/10.1090/S0025-5718-02-01442-4
- MathSciNet review: 1954974