A computable abosolutely normal Liouville number

BECHER, VERÓNICA

Singapur

Conferencia; Algorithmic Randomness Programme; 2014

Institute for Mathematical Sciences, National University of Singapore

We proved the following theorem: There is a computable absolutely normal Liouville number. We regard this result as a step into the ancient problem posed by Émile Borel on exhibiting a natural instance of an absolutely normal number. Borel's understanding of ``natural'' may have been towards numbers that can be described geometrically Pi, analytically as e, or algebraically as square root of 2. To our mind, algorithmic descriptions are also explicit, immediate and worthy of investigation. This is joint work between V. Becher, P. Heiber and T. Slaman.