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We construct a series of examples of Calabi-Yau manifolds in an arbitrarydimension and compute the main invariants. In particular, we give higherdimensional generalization of Borcea-Voisin Calabi-Yau threefolds. We give amethod to compute a local zeta function using the Frobenius morphism fororbifold cohomology introduced by Rose. We compute Hodge numbers of theconstructed examples using orbifold Chen-Ruan cohomology.

$L$-functions of higher dimensional Calabi-Yau manifolds of Borcea-Voisin type