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arxiv: 1709.00820 · v2 · pith:RXDP6I6Qnew · submitted 2017-09-04 · 🧮 math.NT

On the distribution of divisors of monic polynomials over function fields

classification 🧮 math.NT
keywords monicclassesdistributiondivisorsfactorsnumberpolynomialsresidue
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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.\;

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