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Friday, April 8, 2016

**Abstract:** In this talk, we outline a result of Pollicott which established the equidistribution of the periodic continued fractions with respect to the Gauss measure when they are ordered according to the length of corresponding closed geodesics on the modular surface. The method of proof involves the study of certain holomorphic families of nuclear operators on the disk algebra, and in particular, the use of their determinants to form the Laplace transforms of sums of functions over the periodic continued fractions.