Zeros of Solutions of a Functional Equation

By Walter Bergweiler, Walter K. Haymana. 2004

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Nevanlinna theory for the $q$-difference operator and meromorphic solutions of $q$-difference equations (2007, background): “Bergweiler and Hayman [2] studied the zero distribution of entire solutions of linear q -diﬀerence equations.”
On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane (2006, background): “[3], [4], [5], [23], [36]), relatively little is known for the growth of meromorphic solutions to even the first order difference equation (1.”