Nevanlinna theory for the q-difference operator and meromorphic solutions of q-difference equations
نویسندگان
چکیده
It is shown that, if f is a meromorphic function of order zero and q ∈ C, then m „ r, f(qz) f(z) « = o(T (r, f)) (‡) for all r on a set of logarithmic density 1. The remainder of the paper consist of applications of identity (‡) 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.
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