Irrationality exponents of semi-regular continued fractions
Daniel Duverney, Iekata Shiokawa
TL;DR
This paper extends the known formula for the irrationality exponent from regular continued fractions to semi-regular continued fractions under specific conditions, broadening the understanding of approximation properties.
Contribution
It demonstrates that the irrationality exponent formula for regular continued fractions also applies to semi-regular continued fractions with certain constraints, a novel generalization.
Findings
The formula for irrationality exponents remains valid for semi-regular continued fractions.
The paper identifies specific conditions under which the formula applies.
It broadens the class of continued fractions for which irrationality exponents are known.
Abstract
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 conditions.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Mathematical and Theoretical Analysis · Advanced Differential Equations and Dynamical Systems