The case for superelliptic curves

TL;DR

This paper advocates for the importance of superelliptic curves, arguing they extend hyperelliptic curve theory and have broad potential applications across mathematics and cryptography.

Contribution

It presents a compelling case that superelliptic curves are the natural extension of hyperelliptic curves for further study and application.

Findings

Superelliptic curves generalize hyperelliptic curves.

They have potential applications in cryptography and physics.

The paper emphasizes their importance for future research.

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.