Mathematical Physics


Zeta Regularization Applied to the Problem of Riemann Hypothesis and the Calculation of Divergent Integrals

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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Submission history

[v1] 27 Jan 2010
[v2] 28 Jun 2010
[v3] 2012-03-11 09:16:42

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