Differential equations defined on algebraic curves

TL;DR

This paper explores a novel class of differential equations derived from algebraic curves, extending the traditional linear constant coefficient differential equations into a broader mathematical framework.

Contribution

It introduces a new approach by associating differential equations with algebraic curves, expanding the scope of differential equation theory.

Findings

Established a correspondence between algebraic curves and differential equations.

Extended classical differential equations to a more general algebraic setting.

Provided foundational insights for future research in algebraic differential equations.

Abstract

The class of ordinary linear constant coefficient differential equations is naturally embedded into a wider class by associating differential equations to algebraic curves.