2020/11/21 by Evan S. Gawlik, Yuji Nakatsukasa, Gawlik, Evan S. +1 · 1 citation
Mathematics · Physics and Astronomy · #30E10 #41A20 #41A50 #Advanced Mathematical Theories and Applications #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Numerical Analysis (math.NA) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2011.10877
openalex publication_date 2020/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In an influential 1877 paper, Zolotarev asked and answered four questions about polynomial and rational approximation. We ask and answer two questions: what are the best rational approximants r and s to √(z) and sign(z) on the unit circle (excluding certain arcs near the discontinuities), with the property that |r(z)|=|s(z)|=1 for |z|=1? We show that the solutions to these problems are related to Zolotarev's third and fourth problems in a nontrivial manner.