On quantitative analogues of the Goldbach and twin prime conjectures over Fq[t]
Abstract
We study the number of ways to decompose a monic polynomial in Fq[t] of degree n as a sum of two monic irreducible polynomials in Fq[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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