First I will define the regularized determinant for the circle, which is the simplest CY manifold. One can show that any metric on the circle is equivalent under the action of Diff+(S) to the round metric. Thus the only invariant of the metric is the length of the circle. Then we will compute the zeta function of the Laplacian and show how it is related to Riemann zeta function. We will compute the regularized determinant.