Zeta Determinant for Double Sequences of Spectral Type
نویسنده
چکیده
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.
منابع مشابه
Zeta Determinant for Double Sequences of Spectral Type and a Generalization of the Kronecker First Limit Formula
The Kronecker first limit formula in the number field K is an expression of the value of the constant term in the Laurent expansion at s = 1 of the partial Dedekind zeta function ζA(s), associated to an ideal class A of K (see Section 4.1 for details), and has deep applications in number theory. When K is the rational number field or an imaginary quadratic field such formulas are classical and ...
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