Goldbach problem in polynomial values

Abstract

An even integer n ≥ 6 is called a Goldbach number if it is the sum of two odd primes. The Goldbach conjecture says that every even number n ≤ 6 is a Goldbach number. In this paper, we study the mean-square upper bound of the error term related to the Goldbach problem, in polynomial values over short intervals, uniformly with respect to the height of a polynomial of fixed degree. © 1999 Springer.