The Generalized Polynomial Goldbach Problem Original Research Article

In this paper, we are interested by the following generalization for the polynomial Goldbach problem. LetA1,A2, andA3be coprime polynomials in the ring imageq[T]. We ask the question of the representation of a polynomialMset membership, variantimageq[T] as a sum[formula]whereP1,P2,P3are irreducible polynomials subjected to verify some degree conditions. Using the circle method, we get asymptotic estimates for the number of these representations.