Zeta functions on tori using contour integration

Emilio Elizalde, Klaus Kirsten, Nicolas Robles, Floyd Williams

    Research output: Contribution to journalArticleResearchpeer-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 languageEnglish
    Article number1550019
    JournalInternational Journal of Geometric Methods in Modern Physics
    Volume12
    Issue number2
    DOIs
    Publication statusPublished - 1 Jan 2015

    Keywords

    • functional determinants
    • spectral theory
    • Tori
    • zeta functions

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