Picard Values of Entire Functions and Their Differences

This paper studies value distribution of entire function f(z) and their forward differences $$\Delta ^{n}f(z)$$ . We mainly prove: let $$n\in {\mathbb {N}}$$ , f(z) be a transcendental entire function such that f(z) and $$\Delta ^{n}f(z)$$ have finitely many zeros without growth condition, then the exact forms of f(z) and $$\Delta ^{n}f(z)$$ are given.