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 | |
| Publication status | Published - 1 Jan 2015 |
Keywords
- functional determinants
- spectral theory
- Tori
- zeta functions
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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), [1550019]. https://doi.org/10.1142/S021988781550019X