We apply Nevanlinna's value distribution theory to show that some functional equations of Diophantine type have no admissible meromorphic solutions. This result confirms a recent conjecture of Li and Yang.
We establish a q-shift difference analogue of the logarithmic derivative lemma. We also investigate the value distributions of q-shift difference polynomials and the growth of solutions of complex q-shift difference equations.
Atsuji proposed some integrals along Brownian paths to study the Nevanlinna characteristic function T(f,r) when f is meromorphic in the unit disk D. We show that his criterios does not apply to the basic case when f is a modular elliptic function. The divergence of similar integrals computed along the geodesic flow is also proved. (A)