The case for superelliptic curves

2015/02/25 by Tony Shaska, Shaska, Tony, Eustrat Zhupa +3 · 1 citation
Mathematics · #14-01 (Primary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #math.AG #msc:14-01

paper · pdf · doi:10.48550/arxiv.1502.07249

arxiv created 2015/02/25 · openalex publication_date 2015/02/25 · arxiv updated 2015/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

There is a natural question to ask whether the rich mathematical theory of the hyperelliptic curves can be extended to all superelliptic curves. Moreover, one wonders if all of the applications of hyperelliptic curves such as cryptography, mathematical physics, quantum computation, diophantine geometry, etc can carry over to the superelliptic curves. In this short paper we make the case that the superelliptic curves are exactly the curves that one should study.

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