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

Access to Document

10.1142/S021988781550019X

Cite this

@article{b61a5fcc258243949f137f79cc31f20f,

title = "Zeta functions on tori using contour integration",

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.",

keywords = "functional determinants, spectral theory, Tori, zeta functions",

author = "Emilio Elizalde and Klaus Kirsten and Nicolas Robles and Floyd Williams",

year = "2015",

month = jan,

day = "1",

doi = "10.1142/S021988781550019X",

language = "English",

volume = "12",

journal = "International Journal of Geometric Methods in Modern Physics",

issn = "0219-8878",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "2",

}

TY - JOUR

T1 - Zeta functions on tori using contour integration

AU - Elizalde, Emilio

AU - Kirsten, Klaus

AU - Robles, Nicolas

AU - Williams, Floyd

PY - 2015/1/1

Y1 - 2015/1/1

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

M3 - Article

VL - 12

JO - International Journal of Geometric Methods in Modern Physics

JF - International Journal of Geometric Methods in Modern Physics

SN - 0219-8878

IS - 2

M1 - 1550019

ER -

Zeta functions on tori using contour integration

Abstract

Keywords

Access to Document

Fingerprint

Cite this