# Does Chowla's conjecture on the Liouville function imply the Riemann hypothesis?

A paper see here on arXiv claims that Chowla's conjecture (applied to the Liouville function instead of the Mobius function), i.e., that $$\lim_{N\rightarrow \infty} \sum_{n\leq N} \lambda(n+a_1) \lambda(n+a_2) \cdots \lambda(n+a_k)=o(N),$$ implies the Riemann hypothesis. I have been unable to find any references to this claim after some research.

Is this claim new? Any pointers, references appreciated.

This property should be named after Littlewood (the property says: the partial sum up to $$x$$ is $$o(x^{1/2+\epsilon})).$$ The reason for that is due to the fact that this property is valid for Möbius and Louville by Littlewood criterion which use of-course that the Möbius or Louville are multiplicatives. Let us notice furthermore that his example is not multiplicative! On the other hand, as proved by Denjoy in Comptes Rendus Acad. Sci. Paris 192 (1931), 656–658, RH holds almost surely for model which is more close to the zeta.