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On the linear independence measure of logarithms of rational numbers. (English) Zbl 1099.11037

Summary: 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.

MSC:

11J82 Measures of irrationality and of transcendence
11J86 Linear forms in logarithms; Baker’s method
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