Fix positive integers and a prime power . Let
.
An -dimensional -linear subspace of
is said to be *-splitting* if

Concerning splitting subspaces, Niederreiter asked the following

**Question.** Given
such that
, what is the number of
-dimensional -splitting subspaces of
?

This question has been open for over 15 years. We will outline some recent progress as well as connections
to topics such as Singer cycles (in general linear groups), linear recurrences, and primitive polynomials.
En route, we will also notice an amusing connection with the Riemann zeta function and questions such as when
are two polynomials in
of a given positive degree relatively prime.