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Zeta functions on tori using contour integration


Elizalde, Emilio; Kirsten, Klaus; Robles, Nicolas; Williams, Floyd (2014). Zeta functions on tori using contour integration. International Journal of Geometric Methods in Modern Physics:online.

Abstract

A new, seemingly useful presentation of zeta functions on complex tori is derived by using contour integration. It is shown to agree with the one obtained by using the Chowla–Selberg series formula, for which an alternative proof is thereby given. In addition, a new proof of the functional determinant on the torus results, which does not use the Kronecker first limit formula nor the functional equation of the non-holomorphic Eisenstein series. As a bonus, several identities involving the Dedekind eta function are obtained as well.

Abstract

A new, seemingly useful presentation of zeta functions on complex tori is derived by using contour integration. It is shown to agree with the one obtained by using the Chowla–Selberg series formula, for which an alternative proof is thereby given. In addition, a new proof of the functional determinant on the torus results, which does not use the Kronecker first limit formula nor the functional equation of the non-holomorphic Eisenstein series. As a bonus, several identities involving the Dedekind eta function are obtained as well.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2014
Deposited On:29 Jan 2015 16:14
Last Modified:08 Dec 2017 10:33
Publisher:World Scientific Publishing
ISSN:0219-8878
Publisher DOI:https://doi.org/10.1142/S021988781550019X

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