Computational Methods and Function Theory 9 (2009), No. 2, 565--578
Copyright Heldermann Verlag 2009
James Langley
jkl@maths.nott.ac.uk , University of Nottingham, School of Mathematical Sciences, NG7 2RD, U.K.
An estimate is obtained for the growth of a meromorphic function near to a logarithmic singularity of the derivative. This estimate is applied to show that if f is meromorphic of finite lower order in the plane, such that the second derivative f'' has finitely many zeros and the multiplicities of the poles z of f grow at most polynomially in |z|, then f has finitely many poles. Subsequent results then consider the zeros of linear differential polynomials F = f(k) + ak-1 f(k-1) + ... + a0 f, where f is transcendental and meromorphic of finite order in the plane, and the coefficients aj are constants.
Keywords: Meromorphic functions, logarithmic singularities, zeros of derivatives.
MSC 2000: 30D35.
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