# The Problem of Differentiation of Hyperelliptic Functions

## TL;DR

This paper presents a new explicit method for differentiating hyperelliptic functions, extending classical solutions from genus 1 to higher genera, with potential applications in complex analysis and algebraic geometry.

## Contribution

It introduces a novel construction for explicit differentiation of hyperelliptic functions for arbitrary genus, building upon and generalizing previous genus 1 to 3 solutions.

## Key findings

- Explicit differentiation formulas for hyperelliptic functions of higher genus
- Extension of classical genus 1 solutions to genus 2 and 3
- A general method applicable to arbitrary genus

## Abstract

In this work we describe a construction that leads to an explicit solution of the problem of differentiation of hyperelliptic functions. A classical genus $g=1$ example of such a solution is a result of F.G.Frobenius and L.Stickelberger. Our method follows the works that led to constructions of explicit solutions of the problem for genus $g=2$ and $g=3$.