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Mathematics > Complex Variables
Title: A note on Rational Functions with three branched points on the Riemann sphere
(Submitted on 13 Jan 2024 (v1), last revised 2 Apr 2024 (this version, v6))
Abstract: Studying the existence of rational functions with given branched data is a classical problem in the field of complex analysis and algebraic geometry. This problem dates back to Hurwitz and remains open to this day. In this paper, we utilize complex analysis to establish a property of rational functions with three branched points on the Riemann sphere. As applications, we present some new types of exceptional branched data. These results cover some previous results mentioned in \cite{EKS84,PP06,Zhu19}. We also establish the existence of a certain type of rational functions on the Riemann sphere.
Submission history
From: Zhi Qiang Wei [view email][v1] Sat, 13 Jan 2024 02:38:44 GMT (10kb)
[v2] Wed, 24 Jan 2024 03:59:20 GMT (10kb)
[v3] Mon, 29 Jan 2024 10:35:00 GMT (10kb)
[v4] Thu, 1 Feb 2024 03:46:10 GMT (10kb)
[v5] Wed, 27 Mar 2024 05:00:59 GMT (10kb)
[v6] Tue, 2 Apr 2024 06:29:13 GMT (10kb)
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