Nevanlinna's counting functions for difference operators and related results

The study of the Nevanlinna theory for difference operators was introduced independently by Halburd & Korhonen and Chiang & Feng in the years ۲۰۰۶ and ۲۰۰۸ respectively. Halburd and Korhonen proved the uniqueness theorem for meromorphic functions associated with c-separated pairs. In this paper, we have generalised the result by introducing c-separated pairs of multiplicity p and their counting functions. We have deduced some analogues of certain unique results of classical Nevanlinna theory due to Chen, Chen & Tsai; Gopalakrishna & Bhoosnurmath; and Lahiri & Pal. Thereafter, we have also discussed certain implications of the deduced results.

Keywords:

meromorphic functions , c-separated pairs , Nevanlinna's counting functions , difference operator , periodic functions