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arXiv · hep-th/9910097

Spectral Zeta Functions for a Cylinder and a Circle

V. V. Nesterenko·I. G. Pirozhenko
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Abstract

Spectral zeta functions $ζ(s)$ for the massless scalar fields obeying the Dirichlet and Neumann boundary conditions on a surface of an infinite cylinder are constructed. These functions are defined explicitly in a finite domain of the complex plane s containing the closed interval of real axis $-1\le$ Re $s \le 0$. Proceeding from this the spectral zeta functions for the boundary conditions given on a circle (boundary value problem on a plane) are obtained without any additional calculations. The Casimir energy for the relevant field configurations is deduced.

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V. V. Nesterenko, I. G. Pirozhenko. 2007-01-26. Spectral Zeta Functions for a Cylinder and a Circle. https://doi.org/10.1063/1.533358

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