A review on recent results of the $ζ$-function regularization procedure in curved spacetime

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Some recent (1997-1998) theoretical results concerning the $ζ$-function regularization procedure used to renormalize, at one-loop, the effective Lagrangian, the field fluctuations and the stress-tensor in curved spacetime are reviewed.
References added, 9 pages, latex, no figures, contributed to 13th National Conference on General Relativity, Bari, Italy, 21-24 Sep 1998

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