# Casimir Energy of the Laplacian on a Riemannian Manifold

Special principles of ghostly zeta function on Riemannian repeat have happened computed utilizing miscellaneous mathematical approximation blueprints. The parts of few of those principles are of fundamental significance in quantity field hypothesis. A particular advantage of interest in this place stage is the Casimir strength outlined, mathematically, via the ghostly zeta function as a function on the set of versification on the many by (−12) [1,2] and [3]. In this affiliate, a comprehensive form for calculating the Casimir strength of the Laplacian on the whole n-spatial circle, Sn by break the spectral zeta function through the Riemann zeta function is discussed. The ghostly zeta function of the Laplacian maybe computed utilizing this arrangement on a difference of various Riemannian repeat.

**Author(s) Details:**

Louis Omenyi,

Department of Mathematics and Statistics, Alex Ekwueme Federal University, Ndufu-Alike, Nigeria.

**Please see the link here: **https://stm.bookpi.org/RHMCS-V4/article/view/9160

**Keywords: **Laplacian, spectral zeta function, riemann zeta function, casimir energy