Variants of the Barban-Montgomery-Hooley formula in additive number theory

The variance of the distribution of the prime numbers in arithmetic progressions has been studied by Barban, Davenport and Halberstam, and then by Montgomery, Hooley and others. In this talk we shall describe joint work with R.C. Vaughan, leading to related results for the numbers that are representable as the sum of two positive cubes as well as other sequences that are of familiarity in additive number theory.