Proof of Markov’s Theorem

Martin Aigner
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Martin Aigner: Freie Universität Berlin, Fachbereich Mathematik und Informatik Institut für Mathematik

Chapter 9 in Markov's Theorem and 100 Years of the Uniqueness Conjecture, 2013, pp 185-206 from Springer

Abstract: Abstract Let us recall the content of Markov’s theorem. Suppose $$\alpha = [{a_0}, {a_1}, {a_2},\dots]$$ is an irrational number. We set $$\lambda_{n}(\alpha) = {\alpha}_{n+1} + \frac{1} {{\beta}_{n}} \ (n \geq 1),$$ Where $${\alpha}_{n+1} = [a_{n+1}, a_{n+2},\dots], {\beta}_{n} = [{a_n}, a_{n-1},\dots,{a_1}]$$ .

Date: 2013
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DOI: 10.1007/978-3-319-00888-2_9

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