Irreducibility of Chebyshev-Lissajous polynomials
Hanxiong Zhang
TL;DR
This paper investigates the irreducibility of Chebyshev-Lissajous polynomials, confirming two conjectures and enhancing understanding of their algebraic properties over real and complex fields.
Contribution
It proves the irreducibility of Chebyshev-Lissajous polynomials over both real and complex numbers, resolving two existing conjectures.
Findings
Confirmed the irreducibility of Chebyshev-Lissajous polynomials
Validated two conjectures by Merino
Enhanced understanding of polynomial algebra related to Lissajous curves
Abstract
We study certain kind of polynomials associated with Lissajous curves, called Chebyshev-Lissajous polynomials. We investigate their irreducibilities over the real numbers and complex numbers, thus comfirming two conjectures proposed by Merino.
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Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · Mathematical functions and polynomials