Complete determination of the singularity structure of zeta functions
High Energy Physics - Theory
2008-11-26 v2 funct-an
Functional Analysis
Abstract
Series of extended Epstein type provide examples of non-trivial zeta functions with important physical applications. The regular part of their analytic continuation is seen to be a convergent or an asymptotic series. Their singularity structure is completely determined in terms of the Wodzicki residue in its generalized form, which is proven to yield the residua of all the poles of the zeta function, and not just that of the rightmost pole (obtainable from the Dixmier trace). The calculation is a very down-to-earth application of these powerful functional analytical methods in physics.
Keywords
Cite
@article{arxiv.hep-th/9608056,
title = {Complete determination of the singularity structure of zeta functions},
author = {E. Elizalde},
journal= {arXiv preprint arXiv:hep-th/9608056},
year = {2008}
}
Comments
LaTeX, 10 pages, a couple of typos corrected