Generic properties of Pad\'e approximants and Pad\'e universal series
  We establish properties concerning the distribution of poles of Pad e approximants, which are generic in Baire category sense. We also investigate Pad e universal series, an analog of classical universal series, where Taylor partial sums are replaced with Pad e approximants. In particular, we complement previous studies on this subject by exhibiting dense or closed infi nite dimensional linear subspaces of analytic functions in a simply connected domain of the complex plane, containing the origin, whose all non zero elements are made of Pad e universal series. We also show how Pad e universal series can be built from classical universal series with large Ostrowski-gaps. 
St\'ephane Charpentier (I2M), Vassili Nestoridis (MPLA), Franck   Wielonsky (I2M)
math.FA math.CA