Transfer Operator of the Gauss Map

I found out that a Professor of mine, Jean Pestieau, is an academic descendant of Carl Friedrich Gauss. Of course Gauss had 8 students and 43374 descendants. But nevertheless I am proud of Professor Jean Pestieau. He works at the Université Catholique de Louvain.

Professor Gauss invented a map:

h(x) = 1/x - [1/x]

Where [ ] represents the integer part.

It happens that the Transfer Operator of this map, called the Gauss-Kuzmin-Wirsing (GKW) operator, is so difficult, that it has not been fully solved. The theory of the GKW dates back to a hypothesis by Gauss on continued fractions and is closely related to the Riemann zeta function.

Deep mysteries of number theory.