Algebraic Independence and Mahler's method

We give some new results on algebraic independence within Mahler’s method, including algebraic independence of values at transcendental points. We also give some new measures of algebraic independence for infinite series of numbers. In particular, our results furnishes, for $n\ge 1$ arbitrarily large, new examples of sets $({\theta }_1,\mathrm{.}\mathrm{.}\mathrm{.},{\theta }_n)\in {\text{mrr}}^n$ normal in the sense of definition formulated by Grigory Chudnovsky (1980).