scholarly journals Painleve I, Coverings of the Sphere and Belyi Functions

2013 ◽  
Vol 39 (1) ◽  
pp. 43-74 ◽  
Author(s):  
Davide Masoero
Keyword(s):  
Belyi Functions

scholarly journals Belyi functions for Archimedean solids

2000 ◽  
Vol 217 (1-3) ◽  
pp. 249-271 ◽  
Author(s):  
Nicolas Magot ◽  
Alexander Zvonkin
Keyword(s):  
Archimedean Solids ◽  
Belyi Functions

scholarly journals On Rational Functions with More than Three Branch Points

2020 ◽  
Vol 27 (02) ◽  
pp. 231-246
Author(s):  
Jijian Song ◽  
Bin Xu
Keyword(s):  
Positive Integer ◽  
Rational Function ◽  
Riemann Sphere ◽  
Rational Functions ◽  
Branch Points ◽  
New Class ◽  
Belyi Functions

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 Λ 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.

Homology, Belyî functions and canonical curves

1996 ◽  
Vol 90 (1) ◽  
pp. 489-509 ◽  
Author(s):  
Manfred Streit
Keyword(s):  
Canonical Curves ◽  
Belyi Functions

Belyi Functions, Hypermaps and Galois Groups

1996 ◽  
Vol 28 (6) ◽  
pp. 561-590 ◽  
Author(s):  
Gareth Jones ◽  
David Singerman
Keyword(s):  
Galois Groups ◽  
Belyi Functions
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