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math.NT2022★ 1 cited
Continuants and convergence of certain continued fractions
Daniel Duverney, Iekata Shiokawa
We give a concise introduction to the theory of continuants and show how Perron used them in his proof of Tietze theorem on the convergence of infinite semi-regular continued fract…
math.NT2022
A new proof of a theorem of Tietze
Daniel Duverney, Iekata Shiokawa
We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.
math.NT2022
Irrationality exponents of semi-regular continued fractions
Daniel Duverney, Iekata Shiokawa
We prove that the formula giving the exact value of the irrationality exponent of regular continued fractions remains valid for semi-regular continued fractions satisfyiong certain…