# On the enumeration of the roots of arbitrary separable equations using HW hyper-Lambert maps

## TL;DR

This paper introduces a method using HW hyper-Lambert maps to effectively enumerate roots of arbitrary separable equations by projecting onto the Riemann surface, offering a new approach to root finding.

## Contribution

It presents a novel application of HW maps for root enumeration of arbitrary equations, linking roots to projections on Riemann surfaces.

## Key findings

- Effective enumeration of roots via HW maps
- Roots correspond to projection points on Riemann surfaces
- Method applicable to arbitrary separable equations

## Abstract

In this article we use the HW maps to solve arbitrary equations f=0, by providing an effective enumeration of the roots of f, as these project on and at the branches of the HW maps. This is just an enumeration of the projection points (roots) of a pin-line on the Riemann surface of f through HW.