Abstract. In this paper we consider the cohomology of a closed arithmetic hyperbolic 3-manifold with coefficients in the local system defined by the even symmetric powers of the standard representation of SL(2, C). The cohomology is defined over the integers and is a finite abelian group. We show that the order of the 2nd cohomology grows exponentially as the local system grows. We also consider the twisted Ruelle zeta function of a closed arithmetic hyperbolic 3-manifold and we express the leading coefficient of its Laurent expansion at the origin in terms of the orders of the torsion subgroups of the cohomology.

The result is a generalization of the formerly known result for the paraxial magnification matrix for infinite object distance. The effect of the finite object distance correction is small but not negligible. Moreover, the methods for deriving this result serve as a starting point for an even more general treatment of oblique incidence in a future work.

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The result is a generalization of any of the formerly known results for the magnification matrix in the paraxial case. The treatment is complete in the sense that it covers any situation that can be encountered when light propagates through an optical system with a finite number of refracting surfaces to an eye. In particular, the oblique case is treated exactly even if the chief ray lies beyond the domain in which the transference theory of linear optics could be applied.

No abstract