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arXiv · 1709.00534

Cubic Polynomials, Linear Shifts, and Ramanujan Cubics

Gregory Dresden·Prakriti Panthi·Anukriti Shrestha·Jiahao Zhang
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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 $y=x^3$ 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.

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Gregory Dresden, Prakriti Panthi, Anukriti Shrestha, Jiahao Zhang. 2017-09-02. Cubic Polynomials, Linear Shifts, and Ramanujan Cubics. https://arxiv.org/abs/1709.00534

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