  The Minkowski's Question-Mark function is a singular homeomorphism of the
unit interval that maps the set of quadratic surds into the rationals. This
function has deserved the attention of several authors since the beginning of
the twentieth century. Using different representations of real numbers by
infinite sequences of integers, called $\alpha$-L\"uroth expansions, we obtain
different instances of the standard shift map on infinite symbols, all of them
topologically conjugated to the Gauss Map. In this note we prove that each of
these conjugations share properties with the Minkowski's Question-Mark
function: all of them are singular homeomorphisms of the interval, and in the
"rational" cases, they map the set of quadratic surds into the set of rational
numbers. In this sense, this family is a natural generalisation of the
Minkowski's Question-Mark function.
