Nevanlinna theory for the q-difference operator and meromorphic solutions of q-difference equations

It is shown that, if f is a meromorphic function of order zero and q is an element of C, then [GRAPHICS] for all r on a set of logarithmic density 1. The remainder of the paper consists of applications of identity (double dagger) to the study of value distribution of zero-order meromorphic functions, and, in particular, zero-order meromorphic solutions of q-difference equations. The results obtained include q-shift analogues of the second main theorem of Nevanlinna theory, Picard's theorem, and Clunie and Mohon'ko lemmas.