Zeta functions on tori using contour integration
Mathematical Physics
2015-08-10 v1 math.MP
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.
Keywords
Cite
@article{arxiv.1306.4019,
title = {Zeta functions on tori using contour integration},
author = {Emilio Elizalde and Klaus Kirsten and Nicolas Robles and Floyd Williams},
journal= {arXiv preprint arXiv:1306.4019},
year = {2015}
}