On The Hardy-littlewood Problem In Short Intervals

摘要

We study the distribution of Hardy-Littlewood numbers in short intervals both unconditionally and conditionally, i.e. assuming the Riemann Hypothesis (RH). We prove that a suitable average of the asymptotic formula for the number of representations of a Hardy-Littlewood number holds in the interval [n,n + H], where H < X~(1-1/k+∈) and n ∈ [X,2X].