Number Theory

    

A Formula for Mertens' Function and Its Applications

Authors: Roy L. Lewis Jr.

In this article, we prove the limit formula lim M(x) / &pi(x) = lim h / log(x) = 0, h = a constant for Mertens' function M(x) using arithmetic and analytic arguments based on theorems for the prime counting function &pi(x) and the series &sum &mu(k)/k. The formula is evaluated using limit theorems to give: an alternative proof of lim M(x)/ x = 0, a new disproof of Mertens' conjecture, proof of the Odlyzko--te Riele conjecture and a disproof of the Riemann hypothesis based on Littlewood's equivalence theorem.

Comments: 12 Pages.

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Submission history

[v1] 2023-09-03 18:48:27

Unique-IP document downloads: 369 times

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