On Growth of Meromorphic Solutions for Linear Difference Equations. (19th September 2013) - Chen, Zong-Xuan; Shon, Kwang Ho
Abstract : We mainly study growth of linear difference equations P n ( z ) f ( z + n ) + ⋯ + P 1 ( z ) f ( z + 1 ) + P 0 ( z ) f ( z ) = 0 and P n ( z ) f ( z + n ) + ⋯ + P 1 ( z ) f ( z + 1 ) + P 0 ( z ) f ( z ) = F ( z ), where F ( z ), P 0 ( z ), …, P n ( z ) are polynomials such that F ( z ) P 0 ( z ) P n ( z ) ≢ 0 and give the most weak condition to guarantee that orders of all transcendental meromorphic solutions of the above equations are greater than or equal to 1.