On a Goldbach-Type Problem for the Liouville Function

Let λ denote the Liouville function. We show that for all N ≥ 11, the (non-trivial) convolution sum bound align* & |∑n < N λ(n) λ(N-n)| < N-1 align* holds. We also determine all N for which no cancellation in the convolution sum occurs. This answers a question posed at the 2018 AIM workshop on Sarnak’s conjecture.