On Rational Functions with More than Three Branch Points

• 作者: Bin Xu Jijian Song
• 来源期刊: 代数集刊（英文版）
• 关键词: branch data realizability problem Belyi function Riemann's existence theorem
• 年，卷（期）: 2020,（2）
• 页码范围: 231-246
• 页数: 16页
• 语种: 英文
• DOI: 10.1142/S100538672000019X

摘要

Let d be a positive integer and Λ be a collection of partitions of d of the form (a1,...,ap),(b1,...,bq),(m1 + 1,1,...,1),...,(mL + 1,1,...,1),where (m1,...,ml) is a partition of p + q-2 ＞ 0.We prove that there exists a rational function on the Riemann sphere with branch data A if and only if max(m1,...,ml) ＜ d/GCD(a1,...,ap,b1,...,bq).As an application,we give a new class of branch data which can be realized by Belyi functions on the Riemann sphere.