Zeta functions on tori using contour integration

Emilio Elizalde; Klaus Kirsten; Nicolas Robles; Floyd Williams

doi:10.1142/S021988781550019X

Zeta functions on tori using contour integration

Emilio Elizalde, Klaus Kirsten, Nicolas Robles, Floyd Williams

Research output: Contribution to journal › Article › Research › peer-review

Abstract

© 2015 World Scientific Publishing Company. 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.

Original language	English
Article number	1550019
Journal	International Journal of Geometric Methods in Modern Physics
Volume	12
Issue number	2
DOIs	https://doi.org/10.1142/S021988781550019X
Publication status	Published - 1 Jan 2015

Keywords

functional determinants
spectral theory
Tori
zeta functions

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abstract = "{\textcopyright} 2015 World Scientific Publishing Company. 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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AU - Kirsten, Klaus

AU - Robles, Nicolas

AU - Williams, Floyd

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N2 - © 2015 World Scientific Publishing Company. 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.

AB - © 2015 World Scientific Publishing Company. 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.

KW - functional determinants

KW - spectral theory

KW - Tori

KW - zeta functions

U2 - 10.1142/S021988781550019X

DO - 10.1142/S021988781550019X

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JO - International Journal of Geometric Methods in Modern Physics

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