Yik-Man Chiang, University of Science & Technology, Hong Kong

Nevanlinna theory based on Askey-Wilson divided difference operator

Abstract

The idea is to re-write the classical Nevanlinna theory in terms of a divided difference operator due to Askey and Wilson (1985) from special function theory. The Askey-Wilson operator is a q-operator that is more complicated than other q-operators, such as the q-Hahn operator. The operator has close relationship with the Jacobi theta functions. It allows us to derive previously unknown properties for meromorphic functions that have very slow growth in the complex plane. This is a joint work with Shaoji Feng.