Applications of Nevanlinna theory to q-difference equations

Recently Nevanlinna theory (the theory of meromorphic functions) has been used as a detector of integrability of difference equations. In this thesis we study meromorphic solutions of so-called q-difference equations and extend some key results from Nevanlinna theory to the q-difference operator. The Lemma on the Logarithmic Derivative of a meromorphic function has many applications in the study of meromorphic functions and ordinary differential equations. In this thesis, a q-difference analogue of the Logarithmic Derivative Lemma is presented, and then applied to prove a number of results on meromorphic solutions of complex q-difference equations. These results include a difference analogue of the Clunie Lemma, as well as other results on the value distribution of solutions.