Wiman-Valiron method for difference equations

By K. Ishizaki, N. Yanagihara. Nagoya mathematical journal, 2004

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On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane (2006, background): “In fact, it is shown in [26] that logM(r, f) = Lr ( (1 + o(1) ) .”
Zeros of differences of meromorphic functions (2005, methodology): “The following result may be proved using a version of the Wiman–Valiron theory for differences developed in [18]: a proof based instead on the standard Wiman–Valiron theory [14, 22] will be given in Section 5.”
Value distribution of the difference operator (2009, unknown): “Ishizaki and Yanagihara [9] developed a version of Wiman-Valiron theory for difference equations of entire functions of small growth.”
On the growth of logarithmic differences, difference quotients and logarithmic derivatives of meromorphic functions (2006, background): “Halburd and Korhonen established a version of Nevanlinna theory based on diﬀerence operators [16], Bergweiler and Langley [6] considered zeros of diﬀerence operators, and Ishizaki and Yanagihara [26] developed a diﬀerence version of Wiman-Valiron theory for entire functions of small growth.”
Value sharing results for shifts of meromorphic functions (2011, background): “Ishizaki and Yanagihara [9] developed a version of Wiman–Valion theory for difference equations of entire functions of small growth.”