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