Zeta Regularized Determinant of Laplacian

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Can anyone point me to a resource where the zeta regularized determinant of the Laplacian is explicitly computed for simple two dimensional surfaces, say a rectangle or torus or cylinder?

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Such an explicit computation can be found in Section 4 of these lectures. They are a part of of the book "A Window into Zeta and Modular Physics'' edited by K. Kirsten and F. L. Williams.