Lagrange spectrum of a circle over the Eisensteinian field

2020/03/30 by Byungchul Cha, Heather Chapman, Cha, Byungchul +5
Mathematics · #11J06 #11J70 #Analytic Number Theory Research #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2003.13188

openalex publication_date 2020/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study an intrinsic Lagrange spectrum of the unit circle |z|=1 in the complex plane with respect to the Eisensteinian field ℚ(√(-3)). We prove that the minimum of the Lagrange spectrum is 2 and that its smallest accumulation point is 4/√(3). In addition, we characterize the set of all values in the spectrum between 2 and 4/√3.

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