Authors: Jose Javier Garcia Moreta
ABSTRACT: In this paper we review some results of our previous papers involving Riemann Hypothesis in the sense of Operator theory (Hilbert-Polya approach) and the application of the negative values of the Zeta function (1 s) to the divergent integrals 1 0 s x dx and to the problem of defining a consistent product of distributions of the form ( ) ( ) m n D x D x , in this paper we present new results of how the sums over the non-trivial zeros of the zeta function h( ) can be related to the Mangoldt function 0 (x) assuming Riemann Hypothesis.Throughout the paper we will use the notation ( ) ( ) R s s meaning that we use the zeta regularization for the divergent series 0 s n n s>0 or s=0
Comments: 18 Pages.
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