## Mathematical Essays Dedicated to A. J. MacIntyre |

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A. J. Macintyre a)-index Amer analytic analytic functions argument asymptotic values boundary bounded circle of convergence coefficients completes the proof complex numbers conclude condition conformal mapping Conjecture consider continued fractions convex Corollary deduce defined denote Department of Mathematics domain entire function example exists finite asymptotic value follows function f(z given Hadamard product Hence holds holomorphic hypothesis Iff(z implies inequality integers integral functions J. E. Littlewood Kjellberg Lemma Let f(z lim sup linear log M(r log M(r,f log(l log+ London Math maps meromorphic functions minimum modulus obtain polynomial positive number positive upper density power series Proc proof of Theorem prove Theorem real axis regular result Riemann surface satisfies Section sequence solutions starlike subharmonic functions suppose tend to infinity terms from integers that/(z theory transcendental unit disk upper density virtually isolated singularity zero