Resumen de On simultaneous uniform approximation to a $p$-adic number and its square

Yann Bugeaud

• Let be a prime number. We show that a result of Teulié is nearly best possible by constructing a -adic number such that and are uniformly simultaneously very well approximable by rational numbers with the same denominator. The same conclusion was previously reached by Zelo in his PhD thesis, but our approach using -adic continued fractions is more direct and simpler.