2023/04/26 by Dmitry Gayfulin, Gayfulin, Dmitry
Mathematics · Physics and Astronomy · #11J06 #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #FOS: Mathematics #Number Theory (math.NT) #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.2304.13872
openalex publication_date 2023/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Given an irrational number α consider its irrationality measure function ψα(t)=min1≤ q≤ t, q∈ℤ‖qα‖. The set of all values of λ(α)=(\limsupt→∞ tψα(t))-1 where α runs through the set ℝ∖ℚ is called the Lagrange spectrum \mathbbL. In a paper by Moshchevitin an irrationality measure function ψ[2]α(t)=min1≤ q≤ t, q∈ℤ,q≠ qi‖qα‖ was introduced. In other words, we consider the best approximations by fractions, whose denominators are not the denominators of the convergents to α. Replacing the function ψα in the definition of \mathbbL by ψ[2]α, one can get a set \mathbbL2 which is called the ''second'' Lagrange spectrum. In this paper we give the complete structure of discrete part of \mathbbL2.