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Authors:P. C. Fenton
Affiliation:Department of Mathematics, University of Otago, P.O. Box 56, Dunedin, New Zealand
Abstract:
It is shown that if, for an entire function,

begin{displaymath}liminf_{rtoinfty} logEM(r)/r^{lambda} = 0 end{displaymath}

where $0< lambda <1$, then

begin{displaymath}limsup_{rtoinfty}(log m(r)-cospilambdalog M(r))/log r = infty. end{displaymath}

In the proof, the zeros of the function are redistributed to minimize the large values of $log m(r) -cospilambdalog M(r)$.

Keywords:
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