Summatory Mobius Function, and Summatory Liouville Function
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.
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