Uniqueness Theorems on Difference Monomials of Entire Functions

Abstract EN

The aim of this paper is to discuss the uniqueness of the difference monomials fnf(z+c).

It assumed that f and g are transcendental entire functions with finite order and Ek)(1,fnf(z+c))=Ek)(1,gng(z+c)), where c is a nonzero complex constant and n, k are integers.

It is proved that if one of the following holds (i) n≥6 and k=3, (ii) n≥7 and k=2, and (iii) n≥10 and k=1, then fg=t1 or f=t2g for some constants t2 and t3 which satisfy t2n+1=1 and t3n+1=1.

It is an improvement of the result of Qi, Yang and Liu.