On the Liouville function in short intervals

Jake Chinis

Let $\lambda$ denote the Liouville function. Assuming the Riemann Hypothesis, we prove that $${\int }_X^{2X}|\sum _{x\le n\le x+h}\lambda (n){|}^{2}dx\ll Xh(\log X{)}^6,$$ as $X\rightarrow…