Vol. 43, No. 2, 1972

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Zeros of sums of series with Hadamard gaps

Linda Ruth Sons

Vol. 43 (1972), No. 2, 515–524
Abstract

If f is a function of the complex variable z in the unit disc and the power series expansion for f about zero can be expressed as a finite sum of series with Hadamard gaps, then f(z) assumes every finite value infinitely often provided the coefficients in the power series expansion of f do not tend to zero and the average value of (log +1|f(rei𝜃)|)p does not grow too rapidly as r 1 for some p > 1.

Mathematical Subject Classification
Primary: 30A70
Milestones
Received: 2 September 1970
Revised: 4 August 1972
Published: 1 November 1972
Authors
Linda Ruth Sons