Some Statistical Problems Of Prime Polynomials Over Finite Fields

In this paper,we mainly study the statistical asymptotic properties of prime poly-nomials over finite fields.Firstly,the convergence of additive functions is discussed and the central limit theorem of additive functions is obtained.Secondly,the convergence of s-tochastic processes is further studied,and the functional central limit theorem is obtained.Finally,in order to understand more specifically the central limit theorem of additive functions,Erdos-Kac theorem on polynomial rings is proved by Stein's method.