Abstract
We give lower and upper bounds of the irrationality exponent of general continued fractions satisfying certain conditions. Using it we estimate the irrationality exponents of continued fractions representing numbers related with Cahen’s constant and deduce their transcendence from Roth’s theorem.
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Acknowledgements
The authors thank the referees for correcting mistakes and many useful remarks, in particular for suggesting the possibility of the alternative proof given in Sect. 5.
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Communicated by Ilse Fischer.
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Duverney, D., Shiokawa, I. Irrationality exponents of numbers related with Cahen’s constant. Monatsh Math 191, 53–76 (2020). https://doi.org/10.1007/s00605-019-01335-0
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DOI: https://doi.org/10.1007/s00605-019-01335-0