Zeta determinant for double sequences of spectral type

Details Zeta determinant for double sequences of spectral type Zeta determinant for double sequences of spectral type

2006-07-31

arxiv.org/abs/math/0607816v4

Mathematics

Differential Geometry

Scientific paper

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.

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