Belyi Maps from Zeroes of Hypergeometric Polynomials

The evaluation of low-degree hypergeometric polynomials to zero defines algebraic hypersurfaces in the affine space of the free parameters and the argument of the hypergeometric function. This article investigates the algebraic surfaces defined by the hypergeometric equation F12(−N,b;c;z)=0 with N=3...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 13; no. 1; p. 156
Main Author: Vidunas, Raimundas
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.01.2025
Subjects:
Algebra
Analysis
Belyi map (of genus 0)
elliptic surfaces
Enumeration
Functions, Hypergeometric
Gauss hypergeometric function
Hypergeometric functions
Hyperspaces
Mappings (Mathematics)
Mathematical analysis
Mathematical problems
Polynomials
Lithuania
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary:The evaluation of low-degree hypergeometric polynomials to zero defines algebraic hypersurfaces in the affine space of the free parameters and the argument of the hypergeometric function. This article investigates the algebraic surfaces defined by the hypergeometric equation F12(−N,b;c;z)=0 with N=3 or N=4. As a captivating application, these surfaces parametrize certain families of genus 0 Belyi maps. Thereby, this article contributes to the systematic enumeration of Belyi maps.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math13010156