English

Summatory Mobius Function, and Summatory Liouville Function

General Mathematics 2012-12-18 v2

Abstract

The orders of magnitudes of the summatory Liouville function L(x), and the summatory Mobius function M(x), are unconditionally proven to be of the forms L(x) = O(x^.5)), and M(x) = O(x^.5) respectively. Furthermore, applications of these estimates to zeta functions and L-functions are also considered.

Keywords

Cite

@article{arxiv.1106.1895,
  title  = {Summatory Mobius Function, and Summatory Liouville Function},
  author = {N. A. Carella},
  journal= {arXiv preprint arXiv:1106.1895},
  year   = {2012}
}

Comments

13 Pages, Improvements of Lemma 9, and a second proof of Theorem 12 is included in Section 5

R2 v1 2026-06-21T18:20:12.394Z