Computations of the Mertens Function and Improved Bounds on the Mertens Conjecture

Greg Hurst

The Mertens function is defined as $M(x)={\sum }_{n\le x}\mu (n)$, where $\mu (n)$ is the Möbius function. The Mertens conjecture states $|M(x)/\sqrt{x}|<1$ for $x>1$, which was pr…