Complete set of Pure Gaps in Function Fields

2023/04/07 by Alonso S. Castellanos, Castellanos, Alonso S., Erik A. R. Mendoza +3 · 1 citation
Computer Science · Mathematics · #Coding theory and cryptography #Algebraic Geometry and Number Theory #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.2304.03846

Abstract

In this work, we provide a way to completely determine the set of pure gaps G₀(P₁, P₂) at two rational places P₁, P₂ in a function field F over a finite field \mathbbF_q, and its cardinality. Furthermore, we given a bound for the cardinality of the set G₀(P₁, P₂) 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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