Zeros of Sections of Power Series

Introduction....Pages 1-7
Statements of our results....Pages 7-25
Discussion of our numerical results....Pages 26-40
Outline of the method....Pages 41-43
Notational conventions....Pages 43-44
Properties of the Mittag-Leffler function of order 1 < λ<∞....Pages 44-49
Estimates for G m (w) and Q m (w)....Pages 49-52
A differential equation....Pages 53-60
Estimates for J m (w) near the circumference |w|=1....Pages 60-62
Existence and uniqueness of the Szegö curve....Pages 62-63
Crude estimates for |U m (w)| and |Q m (w)|....Pages 63-69
Proof of Theorem 5....Pages 70-70
Proof of Theorem 1....Pages 70-72
Proof of Theorem 2....Pages 72-77
The circular portion of the Szegö curve (Proof of Theorem 3)....Pages 77-79
Proof of Theorem 4....Pages 80-82
Proof of Theorem 6....Pages 82-87
Properties of £-functions; proof of assertion I of Theorem 7....Pages 87-91
£-functions of genus zero are admissible in the sense of Hayman....Pages 91-92
The functions U m (w), Q m (w), G m (w) associated with £-functions of genus zero....Pages 92-94
Estimates for U m (w)....Pages 95-98
Determination of lim Ω m (ζ)....Pages 99-101
Comparison with integrals; proof of assertion II of Theorem 7....Pages 101-102
The Szegö curves for £-functions of genus zero....Pages 103-106
Estimates for U m (σ m e iφ w)....Pages 106-107
Proof of assertion IV of Theorem 7....Pages 108-108