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Belyi Maps from Zeroes of Hypergeometric Polynomials

Author

Listed:
  • Raimundas Vidunas

    (Institute of Applied Mathematics, Vilnius University, 03225 Vilnius, Lithuania)

Abstract

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 F 1 2 ( − 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.

Suggested Citation

  • Raimundas Vidunas, 2025. "Belyi Maps from Zeroes of Hypergeometric Polynomials," Mathematics, MDPI, vol. 13(1), pages 1-30, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:1:p:156-:d:1559881
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