SEMINAR ANNOUNCEMENT - Mathematics
On the metric theory of continued fractions in the field of formal Laurent series over a finite field
Abstract: The fields of formal Laurent series over finite fields, or the non-Archimedean local fields of positive characteristic, are considered to be the true analogues of the real numbers. In this setting, I will introduce the continued fraction algorithm, which is analogous to the classical real case, and ask some metrical questions regarding the averages of partial quotients of continued fraction expansion. In this talk, we shall see that the continued fraction map in positive characteristic is exact with respect to Haar measure. This fact of exactness implies a number of strictly weaker properties. Indeed, we shall use weak mixing and ergodicity, together with the point-wise subsequence ergodic theorems, to answer our questions. This is a joint work with Radhakrishnan Nair. The talk will be accessible to general maths audience.
February 10, 2016, 13:00, FENS 2008