Cubic Polynomials, Linear Shifts, and Ramanujan Cubics
Number Theory
2022-02-25 v2
Abstract
We show that every monic polynomial of degree three with complex coefficients and no repeated roots is either a (vertical and horizontal) translation of or can be composed with a linear function to obtain a Ramanujan cubic. As a result, we gain some new insights into the roots of cubic polynomials.
Cite
@article{arxiv.1709.00534,
title = {Cubic Polynomials, Linear Shifts, and Ramanujan Cubics},
author = {Gregory Dresden and Prakriti Panthi and Anukriti Shrestha and Jiahao Zhang},
journal= {arXiv preprint arXiv:1709.00534},
year = {2022}
}
Comments
9 pages, bibliography