Goldbach Numbers in Short Intervals -- A Nonnegative Model Approach

Abstract

We decrease the length of the shortest interval for which almost all even integers in it are the sum of two primes. This is achieved by applying a version of the Circle Method that uses two minorants together with a nonnegative model for one of them. Compared to Harman's previous strongest result of this type, we in this way do not need any vector sieve type inequality and so require neither additional majorants nor strong density requirements for the minorants.