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ON THE ZEROS OF LINEAR DIFFERENTIAL POLYNOMIALS WITH SMALL RATIONAL COEFFICIENTS
by
J. K. Langley
BibTeX
@MISC{Langley_onthe,
author = {J. K. Langley},
title = {ON THE ZEROS OF LINEAR DIFFERENTIAL POLYNOMIALS WITH SMALL RATIONAL COEFFICIENTS},
year = {}
}
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Abstract
We prove the following: suppose that J{z) is transcendental and meromorphic of finite order in the plane, and that the linear differential polynomial F(z) is defined by and is non-constant, where ak_j(z),...,ao(z) are rational functions vanishing at infinity. Then implies that N(r,l/(fFF')) = N(r,f) = O(logr). A corresponding result is proved for the case where F =f ' + af, where a is a constant. The problem is related to results of Frank and Hellerstein and others. 1.
