© 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.
|Journal||International Journal of Geometric Methods in Modern Physics|
|Publication status||Published - 1 Jan 2015|
- functional determinants
- spectral theory
- zeta functions
Elizalde, E., Kirsten, K., Robles, N., & Williams, F. (2015). Zeta functions on tori using contour integration. International Journal of Geometric Methods in Modern Physics, 12(2), . https://doi.org/10.1142/S021988781550019X