Speaker: Seonhee Lim, Seoul National University
January 9, 2024 02:30 PM
- 03:30 PM
Abstract:
Baladi and Vallée showed the asymptotic normality of the number of division steps and associated costs in the Euclidean algorithm as a random variable on the set of rational numbers with a bounded denominator based on the transfer operator methods. We extend the result and spectral techniques to the Euclidean algorithm over imaginary quadratic fields by studying the dynamics of the nearest integer complex Gauss map, which is piecewise analytic and expanding but does not have full branch inverse maps. A finite Markov partition with a regular CW-structure enables us to associate the transfer operator acting on a direct sum of C1-spaces, from which we obtain the Gaussian distribution as well as residual equidistribution. (This is joint work with Jungwon Lee and Dohyeong Kim.)