On a Goldbach-type problem for the Liouville function

Abstract

Let $\lambda$ denote the Liouville function. We show that for all sufficiently large integers $N$, the (non-trivial) convolution sum bound $$\left|\sum _{1\le n<N}\lambda (n)\lambda (N-n)\right|<N-1$$ holds. This (essentially) answers a question posed at the 2018 AIM workshop on Sarnak's conjecture.

14 pages; fixed several typos and added a remark, comments welcome