The Energy Spectral Density of the Mertens Function

Abstract

The Mertens function is the summatory Mobius function but the Mertens function can be generated recursively without using this definition. This recursive definition is the basis of autocorrelations that can be done on sequences of Mertens function values. Fourier transforms of the autocorrelations result in the energy spectral density. A likely upper bound of the absolute value of the Mertens function is determined.

Bounds of the Mertens Functions

“…> | ( )| when > 1 with sufficient numerical evidence. More experimental evidence can be found in the work of Cox and Ghosh [18][19] .Using this likely upper bound we showed that we have a sufficient condition to prove the Riemann Hypothesis using the Littlewood condition.…”

Analytical Solution of Burgers Equation using Cole - Hopf Transformation: Part 1

“…Integrating both sides of the above equation we get Some other articles are [17] and [18] and [19] and [20] and [21] and [22] and [23] and [24].…”

Relationship of Galerkin FEM with Central Difference Method

“…Some other articles are [25] and [26] and [27] and [28] and [29] and [30] and [31] and [32] and [60].…”