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arXiv:2310.00326math.HO

The Beauty of Roots

John C. Baez

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Abstract

A "Littlewood polynomial" is a polynomial whose coefficients are all 1 or -1. The set of all complex roots of all Littlewood polynomials exhibits many complicated, beautiful and fascinating patterns. Some fractal regions of this set closely resemble "dragon sets" formed by iterated function systems. A heuristic argument for this is known, but no precise theorem along these lines has been proved. We invite the reader to try.

arXiv comments
Journal reference
Notices Amer. Math. Soc. 70 (2023), 1495-1497
DOI
doi:10.1090/noti2789
Subjects
math.HOHistory and Overview math.COCombinatorics

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