Zeta determinant for double sequences of spectral type

Zeta Determinant for Double Sequences of Spectral Type

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...

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 ...

Spectral analysis and zeta determinant on the deformed spheres

We consider a class of singular Riemannian manifolds, the deformed spheres S k , defined as the classical spheres with a one parameter family g[k] of singular Riemannian structures, that reduces for k = 1 to the classical metric. After giving explicit formulas for the eigenvalues and eigenfunctions of the metric Laplacian ∆SN k , we study the associated zeta functions ζ(s,∆SN k ). We introduce ...

On Zeta Functional Determinant by Sun-yung

Functional equations for double zeta-functions

As the first step of research on functional equations for multiple zeta-functions, we present a candidate of the functional equation for a class of two variable double zeta-functions of the Hurwitz–Lerch type, which includes the classical Euler sum as a special case.