Abstract : Given a fixed integer $q \geq 2$, an irrational number $\xi$ is said to be a $q$-normal number if any preassigned sequence of $k$ digits occurs in the $q$-ary expansion of $\xi$ with the expected frequency, that is $1/q^k$. In this talk, we expose new methods that allow for the construction of large families of normal numbers. This is joint work with Professor Jean-Marie De Koninck.

Keywords : number systems; normal numbers; arithmetic function; $q$-normal number; $q$-ary expansion