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.