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 2006 and 2008 respectively. Halburd and Korhonen proved the unique 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 uniqueness 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.