# using zeta function in the regularization of functional trace and determinant

I'm looking for books or lectures concerning Zeta function regularization. In particular, I'm interested in using zeta function in the regularization of functional trace and determinant . To be more specific, I want to explain in detail two formula

$$\zeta_A(s)=Trace(A^{-s})= \frac{1}{\Gamma(s)} \int_0^\infty t^{s-1} Trace \; e^{-tA} dt$$

$$det A= e^{-\zeta'_A(0)}$$

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Good references and explanations.