Continued fractions in Q_p and applications

Continued fractions are important tools in diophantine approximation and provide also interesting methods to construct transcendental numbers.  The first studies in this direction are due to Liouville, who dealt with unbounded partial quotients, then Maillet and Baker exhibited continued fractions with bounded partial quotients converging to transcendental numbers. Furthermore, Baker's results have been recently improved by several other authors.
In the 1970s, continued fractions were systematically introduced also in the field of p-adic numbers. In this talk, we present an overview about the definition and the main properties of continued fractions in Q_p, focusing then on some new results about transcendence. We conclude the talk highlighting some possible applications in cryptography and related topics.