English

On the Oscillations of Multiplicative Functions Taking Values +/- 1

Number Theory 2007-05-23 v2

Abstract

For completely multiplicative functions f(n) taking values 1 and -1, under certain conditions on f(n) we show that f(n) changes sign at least x exp(-7(log log x)sqrt(log x)) times as n runs through the integers <= x.

Keywords

Cite

@article{arxiv.math/0208213,
  title  = {On the Oscillations of Multiplicative Functions Taking Values +/- 1},
  author = {Ernie Croot},
  journal= {arXiv preprint arXiv:math/0208213},
  year   = {2007}
}

Comments

12 pages, accepted by Journal of Number Theory

R2 v1 2026-07-22T16:47:17.782Z