Representing an element in F_q[t] as the sum of two irreducibles
arXiv:0809.4381 · doi:10.1112/S0025579313000065
Abstract
A monic polynomial in F_q[t] of degree n over a finite field F_q of odd characteristic can be written as the sum of two irreducible monic elements in F_q[t] of degrees n and n-1 if q is larger than a bound depending only on n. The main tool is a sufficient condition for simultaneous primality of two polynomials in one variable x with coefficients in F_q[t].
16 pages. Major revision accepted for publication in Mathematika. This version is slightly different from the one to be published