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arXiv · 2304.03846

Complete set of Pure Gaps in Function Fields

Alonso S. Castellanos·Erik A. R. Mendoza·Guilherme Tizziotti
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Abstract

In this work, we provide a way to completely determine the set of pure gaps $G_0(P_1, P_2)$ at two rational places $P_1, P_2$ in a function field $F$ over a finite field $\mathbb{F}_q$, and its cardinality. Furthermore, we given a bound for the cardinality of the set $G_0(P_1, P_2)$ which is better, in some cases, than the generic bound given by Homma and Kim. As a consequence, we completely determine the set of pure gaps and its cardinality for two families of function fields: the $GK$ function field and Kummer extensions.

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Alonso S. Castellanos, Erik A. R. Mendoza, Guilherme Tizziotti. 2023-04-07. Complete set of Pure Gaps in Function Fields. https://arxiv.org/abs/2304.03846

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