Zeta determinant for double sequences of spectral type
Differential Geometry
2009-05-17 v4 Number Theory
Abstract
We study the spectral functions, and in particular the zeta function, associated to a class of sequences of complex numbers, called of spectral type. We investigate the decomposability of the zeta function associated to a double sequence with respect to some simple sequence, and we provide a technique for obtaining the first terms in the Laurent expansion at zero of the zeta function associated to a double sequence. We particularize this technique to the case of sums of sequences of spectral type, and we give two applications: the first concerning some special functions appearing in number theory, and the second the functional determinant of the Laplace operator on a product space.
Cite
@article{arxiv.math/0607816,
title = {Zeta determinant for double sequences of spectral type},
author = {Mauro Spreafico},
journal= {arXiv preprint arXiv:math/0607816},
year = {2009}
}