Description
The Thue-Morse sequence has partial escape of mass over F2((1/t))
Every Laurent series in the field Fq ((1/t)) has a continued fraction expansion
whose digits are polynomials. De-Mathan and Teulie proved that the degrees of the partial quotients of the left shifts of every quadratic Laurent series are unbounded. Shapira and Paulin improved this by showing that, in fact, a positive proportion of the degrees are bigger than any bound. We show that their result is best possible in the following sense: For the Laurent series over mathbbF2((1/t)) whose sequence of coefficients is the Thue-Morse sequence, this proportion is strictly less than 1. This talk is based on a work in progress with Uri Shapira and Noy Soffer-Aranov.
