A Second Main Theorem on ℙ n for difference operator

Abstract

The main result of this article is an extension of the Second Main Theorem, of Halburd and Korhonen, for meromorphic functions of finite order. Their result replaces the counting function of the ramification divisor Nramf(r) in the classical Second Main Theorem by the counting function of a finite difference divisor Npair(r). In this article, the Second Main Theorem of Halburd and Korhonen is extended to the case of holomorphic maps into ℙn of finite order.