Weierstrass Pure Gaps From a Quotient of the Hermitian Curve

2017/04/11 by Shudi Yang, Yang, Shudi, Chuangqiang Hu +1
Mathematics · #11R58 #14H55 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · pdf · doi:10.48550/arxiv.1705.05213

openalex publication_date 2017/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, by employing the results over Kummer extensions, we give an arithmetic characterization of pure gaps at many totally ramified places over the quotients of Hermitian curves, including the well-studied Hermitian curves as special cases. The cardinality of these pure gaps is explicitly investigated. In particular, the numbers of gaps and pure gaps at a pair of distinct places are determined precisely, which can be regarded as an extension of the previous work by Matthews (2001) considered Hermitian curves. Additionally, some concrete examples are provided to illustrate our results.

Citations

• Algebraic Geometric codes from Kummer Extensions

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• Weierstrass pure gaps on curves with three distinguished points
• Weierstrass points on Kummer extensions
• Weierstrass Semigroup and Pure Gaps at several points on the GK curve
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