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

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.

10 pages

References in corpus (1)

• A potential analogue of Schinzel's hypothesis for polynomials with coefficients in Fq[t]

Cited by in corpus (6)

• On the Bateman-Horn conjecture for polynomials over large finite fields
• Correlation of arithmetic functions over ${\mathbb{F}}_q[T]$
• Cubic twin prime polynomials are counted by a modular form
• Arithmetic correlations over large finite fields
• Prime polynomial values of quadratic functions in short intervals
• Twin prime polynomials in function field