Abstract:

Universal Taylor series (U.T.S) are Taylor series, so that subsequences of their partial sums have nice approximation properties outside the circle of convergence.For universal Taylor series defined on the open unit disk we prove a great type Picard theorem.Universal Taylor series may also be defined on some doubly connected sets, although this is not always the case.We would also like to discuss some methods that have been developed in order to prove the existence or not of U.T.S in some doubly connected sets.Our basic tools in our approach (related to the existence questions) are Baire and Mergelyan's theorems.To prove a great type Picard theorem we use essentially a result about the growth of coefficients of U.T.S