## Summary of the Zeta Regularization Method Applied to the Calculation of Divergent Series and Divergent Integrals

**Authors:** Jose Javier Garcia Moreta

•ABSTRACT: We study a generalization of the zeta regularization method applied to the case of the regularization of divergent integrals for positive ‘s’ , using the Euler Maclaurin summation formula, we manage to express a divergent integral in term of a linear combination of divergent series , these series can be regularized using the Riemann Zeta function s >0 , in the case of the pole at s=1 we use a property of the Functional determinant to obtain the regularization , with the aid of the Laurent series in one and several variables we can extend zeta regularization to the cases of integrals , we believe this method can be of interest in the regularization of the divergent UV integrals in Quantum Field theory since our method would not have the problems of the Analytic regularization or dimensional regularization
•Keywords: = Riemann Zeta function, Functional determinant, Zeta regularization, divergent series .

**Comments:** 20 Pages.

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### Submission history

[v1] 13 Sep 2010

[v2] 8 Nov 2010

[v3] 11 Feb 2011

[v4] 23 Feb 2011

[v5] 2013-05-03 15:35:33

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