On quantitative analogues of the Goldbach and twin prime conjectures over F_q[t]

2009/12/09 by Andreas O. Bender, Paul Pollack, Bender, Andreas O. +1
Mathematics · #11N32 #11T55 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11N32 #msc:11T55

paper · pdf · doi:10.48550/arxiv.0912.1702

10 pages

arxiv created 2009/12/09 · arxiv updated 2010/01/07

Abstract

We study the number of ways to decompose a monic polynomial in F_q[t] of degree n as a sum of two monic irreducible polynomials in F_q[t]. Our principal result is an asymptotic formula for the number of such representations in the case when q is large compared to n. In its range of validity, this formula agrees with what is suggested by heuristic arguments from the rational setting. We also present similar results towards an analogue of the twin prime conjecture.

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