Bounding sums of the Möbius function over arithmetic progressions

Lynnelle Ye

Let $M(x)={\sum }_{1\le n\le x}\mu (n)$ where $\mu$ is the Möbius function. It is well-known that the Riemann Hypothesis is equivalent to the assertion that $M(x)=O(x^{1/2+\epsilon })$ for all $ε>…