Odd order cases of Chowla's averages over arbitrary rectangles

Qiang Huo, Zhengxing Lian, Kangbo Ouyang

Let $\lambda$ be the Liouville function. In this paper we prove an average form of Chowla Conjecture for even $k$. that is, for every fixed even integer $k\ge 2$, we prove that \[ \lim…