$a$-Numbers of Cyclic Degree $p^2$ Covers of the Projective Line
- Resource Type
- Working Paper
- Authors
- Dang, Huy; Groen, Steven R.
- Source
- Subject
- Mathematics - Number Theory
- Language
We investigate the $a$-numbers of $\mathbb{Z}/p^2\mathbb{Z}$-covers in characteristic $p>2$ and extend a technique originally introduced by Farnell and Pries for $\mathbb{Z}/p\mathbb{Z}$-covers. As an application of our approach, we demonstrate that the $a$-numbers of ``minimal'' $\mathbb{Z}/9\mathbb{Z}$-covers can be deduced from the associated branching datum.
Comment: 37 pages. Comments welcome!