2015/01/27 by Janne Gröhn, Artur Nicolau
Mathematics · #Algebraic and Geometric Analysis #Differential (mechanical device) #Differential geometry #Distribution (mathematics) #Geodesic #Geometry #Holomorphic and Operator Theory #Mathematical analysis #Mathematics #Meromorphic and Entire Functions #Physics #Plane (geometry) #Point (geometry) #Pure mathematics #Sequence (biology) #Unit (ring theory) #Zero (linguistics) #math.CA #msc:34C10
paper · pdf · doi:10.1112/blms.12036
published as Uniform separation, hyperbolic geodesics and zero distribution of solutions of linear differential equations, Bull. Lond. Math. Soc. 49 (2017), no. 3, 380-390 · 12 pages
arxiv created 2015/01/27 · openalex publication_date 2017/02/22 · arxiv updated 2018/10/01 · openalex created_date 2021/02/01 · openalex updated_date 2026/08/05
It is shown that a separated sequence of points in the unit disc of the complex plane is in fact uniformly separated if there exists an intermediate sequence, containing a point from each hyperbolic geodesic which connects any two points from the original sequence, and whose separated subsequences are uniformly separated. This result is applied to improve recent results on the zero distribution of solutions of linear differential equations in the unit disc.