Zeros of Sections of Power Series Statements of our results Discussion of our numerical results Outline of the method Notational conventions Properties of the Mittag Leffler function of order 1 < < Estimates for Gm(w) and Qm(w) A differential equation Estimates for Jm(w) near the circumference |w|=1 Existence and uniqueness of the Szegö curve Crude estimates for |Um(w)| and |Qm(w)| Proof of Theorem 5 Proof of Theorem 1 Proof of Theorem 2 The circular portion of the Szegö curve (Proof of Theorem 3) Proof of Theorem 4 Proof of Theorem 6 Properties of £ functions; proof of assertion I of Theorem 7 £ functions of genus zero are admissible in the sense of Hayman The functions Um(w) Qm(w) Gm(w) associated with £ functions of genus zero Estimates for Um(w) Determination of lim m() Comparison with integrals; proof of assertion II of Theorem 7 The Szegö curves for £ functions of genus zero Estimates for Um(meiw) Proof of assertion IV of Theorem 7.