## 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

**Unique-IP document downloads:** 195 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*