On the rational approximation to -adic Thue–Morse numbers
Yann Bugeaud
Institut universitaire de France; Université de Strasbourg, France
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Abstract
Let be a prime number and let be an irrational -adic number. Its multiplicative irrationality exponent is the supremum of the real numbers for which the inequality has infinitely many solutions in nonzero integers and . We show that can be expressed in terms of a new exponent of approximation attached to a sequence of rational numbers defined in terms of . We establish that , where is the -adic number , whose sequence of digits is given by the Thue–Morse sequence over .
Cite this article
Yann Bugeaud, On the rational approximation to -adic Thue–Morse numbers. Rev. Mat. Iberoam. 39 (2023), no. 4, pp. 1349–1371
DOI 10.4171/RMI/1384