Zeros of Sections of Power Series

Inhalt

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(?mei?w).- Proof of assertion IV of Theorem 7.