$a$-Numbers of Cyclic Degree $p^2$ Covers of the Projective Line

Huy Dang; Steven R. Groen

doi:10.1016/j.jnt.2025.05.016

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arXiv · 2309.12153

$a$-Numbers of Cyclic Degree $p^2$ Covers of the Projective Line

Huy Dang·Steven R. Groen

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Abstract

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.

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Huy Dang, Steven R. Groen. 2023-09-21. $a$-Numbers of Cyclic Degree $p^2$ Covers of the Projective Line. https://doi.org/10.1016/j.jnt.2025.05.016

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