Resumen de On the rational approximation to p-adic Thue–Morse numbers

Yann Bugeaud

• Let p be a prime number and let be an irrational p-adic number. Its multiplicative irrationality exponent [expression] f is the supremum of the real numbers [expression] for which the inequality [expression has infinitely many solutions in nonzero integers a and b. We show that [expression] can be expressed in terms of a new exponent of approximation attached to a sequence of rational numbers defined in terms of [expression. We establish that [expression / D 3, where [expression];p is the p-adic number 1 p p 2 C p 3 p 4 C [expression], whose sequence of digits is given by the Thue–Morse sequence over [expression].