On generalized Weierstrass semigroups in arbitrary Kummer extensions of Fq(x)

IF 1.3 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2026-06-01 Epub Date: 2026-02-03 DOI:10.1016/j.ffa.2026.102808

Alonso S. Castellanos , Erik Mendoza , Guilherme Tizziotti

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引用次数: 0

Abstract

In this work, we investigate generalized Weierstrass semigroups in arbitrary Kummer extensions of the rational function field

F_{q} (x)

. We analyze their structure and properties, with a particular emphasis on their maximal elements. Explicit descriptions of the sets of absolute and relative maximal elements within these semigroups are provided. Additionally, we apply our results to function fields of the maximal curves

X_{a, b, n, s}

and

Y_{n, s}

, which cannot be covered by the Hermitian curve, and the Beelen-Montanucci curve. Our results generalize and unify several earlier contributions in the theory of Weierstrass semigroups, providing new perspectives on the relationship between these semigroups and function fields.

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关于Fq(x)的任意Kummer扩展中的广义Weierstrass半群

本文研究了有理函数域Fq(x)的任意Kummer扩展中的广义Weierstrass半群。我们分析了它们的结构和性质，特别强调了它们的最大元素。给出了这些半群中绝对极大元和相对极大元的集合的显式描述。此外，我们将我们的结果应用于最大曲线Xa，b,n，s和Yn，s的函数场，这些函数场不能被厄米曲线和Beelen-Montanucci曲线覆盖。我们的研究结果推广和统一了weerstrass半群理论的一些早期贡献，为研究这些半群与函数场之间的关系提供了新的视角。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.