Quantitative metric theory of continued fractions in positive characteristic

I will speak about the quantitative version of metrical results on the averages of partial quotients of continued fraction expansions in positive characteristic. This is a joint work with Radhakrishnan Nair (Liverpool). The continued fraction map, usually defined to the unit interval, can be generalized to the field of formal power series in finite characteristic. We shall see how this can be done. Then we shall prove the mixing properties of this map and show how ergodic theorems can be used to study the statistical behavior of the associated continued fraction expansions. Finally, we shall introduce Gál and Koksma's method and use it to establish the quantitative metric theory of continued fractions in positive characteristic.

Note: "Positive characteristic" is usually used interchangeably for "a non-Archimedean local field of positive characteristic," or "a field of formal Laurent series over a finite field."