Zeros of sums of series with Hadamard gaps

Linda Ruth Sons

Vol. 43 (1972), No. 2, 515–524

DOI: 10.2140/pjm.1972.43.515

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(re^i𝜃)|)^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