## 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.

**Download:** **PDF**

### Submission history

[v1] 27 Jan 2010

[v2] 28 Jun 2010

[v3] 2012-03-11 09:16:42

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