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Abstract: Hasse–Weil zeta functions of -character varieties of arithmetic two-bridge link groups are determined. Special values of the zeta functions at are also investigated. [Copyright &y& Elsevier]

Abstract: The smallness is proved of étale fundamental groups for arithmetic schemes. This is a higher dimensional analogue of the Hermite–Minkowski theorem. We also refer to the case of varieties over finite fields. As an application, we prove certain finiteness results of representations of the fundamental groups over algebraically closed fields. [Copyright &y& Elsevier]

Abstract: It is proved that the generating function defined by the numbers of isomorphism classes of absolutely irreducible representations of a finitely generated group G into for is a rational function. It is also proved that the generating function defined by weighted sums over isomorphism classes of representations of G into for is meromorphic over both the complex numbers and the p-adic complex numbers. [Copyright &y& Elsevier]