Ebook: Zeros of Sections of Power Series

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Content:
Front Matter....Pages -
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 < ?<?....Pages 44-49
Estimates for Gm(w) and Qm(w)....Pages 49-52
A differential equation....Pages 53-60
Estimates for Jm(w) near the circumference |w|=1....Pages 60-62
Existence and uniqueness of the Szeg? curve....Pages 62-63
Crude estimates for |Um(w)| and |Qm(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 Szeg? 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 Um(w), Qm(w), Gm(w) associated with ?-functions of genus zero....Pages 92-94
Estimates for Um(w)....Pages 95-98
Determination of lim ?m(?)....Pages 99-101
Comparison with integrals; proof of assertion II of Theorem 7....Pages 101-102
The Szeg? curves for ?-functions of genus zero....Pages 103-106
Estimates for Um(?mei?w)....Pages 106-107
Proof of assertion IV of Theorem 7....Pages 108-108
Back Matter....Pages -

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Content:
Front Matter....Pages -
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 < ?<?....Pages 44-49
Estimates for Gm(w) and Qm(w)....Pages 49-52
A differential equation....Pages 53-60
Estimates for Jm(w) near the circumference |w|=1....Pages 60-62
Existence and uniqueness of the Szeg? curve....Pages 62-63
Crude estimates for |Um(w)| and |Qm(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 Szeg? 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 Um(w), Qm(w), Gm(w) associated with ?-functions of genus zero....Pages 92-94
Estimates for Um(w)....Pages 95-98
Determination of lim ?m(?)....Pages 99-101
Comparison with integrals; proof of assertion II of Theorem 7....Pages 101-102
The Szeg? curves for ?-functions of genus zero....Pages 103-106
Estimates for Um(?mei?w)....Pages 106-107
Proof of assertion IV of Theorem 7....Pages 108-108
Back Matter....Pages -
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