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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