Extension of the Titchmarsh representation of the Mertens function M(x), and numerical support of the Riemann hypothesis
A closed form representation of the Mertens function, without assuming simplicity of the non-trivial zeros of the zeta function, is proved and the Titchmarsh representation of the function is recovered as a special case. We exploit a representation of the Mertens function and provide numerical support of the Riemann hypothesis and the simplicity of the zeros of the zeta function. (C) 2008 Elsevier Ltd. All rights reserved.
mertens function riemann hypothesis non-trivial zeros zeta function critical strip critical line mellin transform mobius function