On the Maillet--Baker continued fractions

Details On the Maillet--Baker continued fractions On the Maillet--Baker continued fractions

2005-11-28

arxiv.org/abs/math/0511681v1

Mathematics

Number Theory

Scientific paper

We use the Schmidt Subspace Theorem to establish the transcendence of a class
of quasi-periodic continued fractions. This improves earlier works of Maillet
and of A. Baker. We also improve an old result of Davenport and Roth on the
rate of increase of the denominators of the convergents to any real algebraic
number.

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