On irrationality measure of Thue-Morse constant
Dzmitry Badziahin, Evgeniy Zorin
TL;DR
This paper establishes a new measure of irrationality for the Thue-Morse constant, a specific Mahler number, using infinite product representations, advancing understanding of its approximation properties.
Contribution
It introduces a novel irrationality measure for the Thue-Morse constant within the class of Mahler numbers, expanding the analytical tools available for such constants.
Findings
Derived a non-trivial irrationality measure for the Thue-Morse constant.
Connected the measure to infinite product representations of Mahler numbers.
Enhanced understanding of the approximation properties of the Thue-Morse constant.
Abstract
We provide a non-trivial measure of irrationality for a class of Mahler numbers defined with infinite products which cover the Thue-Morse constant.
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