Yik-Man Chiang, Shao-Ji Feng
Published 2013-09-17, updated 2015-02-11Version 3
This 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.
Comments: Corrected several typos. Added an example showing the estimate given by Theorem 5.2 is sharp in the sense that the error term there no longer hold for entire function of order one
Meromorphic functions of finite $\varphi$-order and linear $q$-difference equations
Two semigroup rings associated to a finite set of germs of meromorphic functions
An old new class of meromorphic functions
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