Partial sums of the M{\"o}bius function
Number Theory
2008-02-13 v2 Classical Analysis and ODEs
Abstract
Assuming the Riemann Hypothesis we establish an upper bound for the sum of the M{\" o}bius function up to . 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.
Cite
@article{arxiv.0705.0723,
title = {Partial sums of the M{\"o}bius function},
author = {K. Soundararajan},
journal= {arXiv preprint arXiv:0705.0723},
year = {2008}
}