Conjectures around the baker-gammel-wills conjecture

Abstract

The Baker-Gammel-Wills Conjecture states that if a functionf is meromorphic in a unit diskD, then there should, at least, exist an infinite subsequenceN ⊆N such that the subsequence of diagonal Pade approximants tof developed at the origin with degrees contained inN converges tof locally uniformly inD/{poles off}. Despite the fact that this conjecture may well be false in the general Pade approximation in several respects. In the present paper, six new conjectures about the convergence of diagonal Pade approximants are formulated that lead in the same direction as the Baker-Gammel-Wills Conjecture. However, they are more specific and they are based on partial results and theoretical considerations that make it rather probable that these new conjectures hold true.