On the growth of logarithmic difference of meromorphic functions and a Wiman-Valiron estimate
Complex Variables
2016-05-02 v4
Abstract
The paper gives a precise asymptotic relation between higher order logarithmic difference and logarithmic derivatives for meromorphic functions with order strictly less then one. This allows us to formulate a useful Wiman-Valiron type estimate for logarithmic difference of meromorphic functions of small order. We then apply this estimate to prove a classical analogue of Valiron about entire solutions to linear differential equations with polynomials coefficients for linear difference equations.
Keywords
Cite
@article{arxiv.1309.4211,
title = {On the growth of logarithmic difference of meromorphic functions and a Wiman-Valiron estimate},
author = {Yik-Man Chiang and Shao-Ji Feng},
journal= {arXiv preprint arXiv:1309.4211},
year = {2016}
}
Comments
Corrected further typos. Revised the error term estimates in Theorem 5.2. Added a dedication, Constructive Approximations (published online 21 January, 2016)