Summatory Mobius Function, and Summatory Liouville Function

Details Summatory Mobius Function, and Summatory Liouville Function Summatory Mobius Function, and Summatory Liouville Function

2011-06-09

arxiv.org/abs/1106.1895v2

Mathematics

General Mathematics

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

Scientific paper

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.

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