A lacunary series is a Taylor series with large gaps between its non-zero coefficients. In this thesis we exploit these gaps to obtain results of linear independence of values of lacunary series at integer points. As well, we will study different methods found in Diophantine approximation which we use to study arithmetic properties of values of lacunary series at algebraic points. Among these methods will be Mahler's method and a new approach due to Jean-Paul Bézivin.

A lacunary series is a Taylor series with large gaps between its non-zero coefficients. In this thesis we exploit these gaps to obtain results of linear independence of values of lacunary series at integer points. As well, we will study different methods found in Diophantine approximation which we use to study arithmetic properties of values of lacunary series at algebraic points. Among these methods will be Mahler's method and a new approach due to Jean-Paul Bézivin.