  Let $k$ be a function field of one variable over a finite field with the
characteristic not equal to two. In this paper, we consider the prehomogeneous
representation of the space of binary quadratic forms over $k$. We have two
main results. The first result is on the principal part of the global zeta
function associated with the prehomogeneous vector space. The second result is
on a mean value theorem for degree zero divisor class groups of quadratic
extensions over $k$, which is a consequence of the first one.

Number Theory