Partial sums of the M{ö}bius function

Abstract

Assuming the Riemann Hypothesis we establish an upper bound for the sum of the M{\" o}bius function up to $x$. Our method is based on estimating the frequency with which intervals of a given length can contain an unusual number of ordinates of zeros of the Riemann zeta-function.

11 pages; AIM preprint number 2007-23; Version 2 makes some expository changes