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.