English

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 xx. 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.

Keywords

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}
}
R2 v1 2026-06-21T08:25:12.845Z