Hayman conjecture in the complex and p-adic fields

Abstract

The purpose of this paper is to establish some
results on the Hayman Conjecture in the complex and p-adic fields. The author discusses the valuesharing problem, some versions of the Hayman conjecture for differential polynomials of the form f n (( f )n1 ) (t1) ...(( f ) nk) (tk) in the complex and p-adic fields, and difference Operators and difference polynomials of the forms P ( f ) (∆1 f )k1 ...(∆q f )kq and P ( f ) ( f (z + e))q1 ...(f (z + kc))qk in a p-adic field.