A mean value theorem for orders of degree zero divisor class groups of quadratic extensions over a function field

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63561Let $k$ 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.30 pagesNumber Theory11M41A mean value theorem for orders of degree zero divisor class groups of quadratic extensions over a function fieldtext