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Eta series and eta invariants of Z4-manifolds

In this paper, for each n = 4r + 3, we construct a family of compact flat spin n-manifolds with holonomy group isomorphic to Z4 such that the spectrum of the Dirac operator D is asymmetric. For these manifolds we will obtain explicit expressions for the eta series, η(s), in terms of Hurwitz zeta functions, and for the eta-invariant, η, associated to D. The explicit expressions will show the meromorphic continuation of η(s) to C is in fact everywhere holomorphic.