On the distribution of divisors of monic polynomials over function fields

Abstract

This paper deals with function field analogues of famous theorems of Laudau which counted the number of integers which have $t$ prime factors and R. Hall which researched the distribution of divisors of integers in residue classes.\;We extend the Selberg-Delange method to handle the following problems.\;The number of monic polynomials with degree $n$ have $t$ irreducible factors;\;The number of monic polynomials with degree $n$ in some residue classes have $t$ irreducible factors and the residue classes distribution of divisors of monic polynomial.\;