2008/11/28 by Raimundas Vidūnas, Vidunas, Raimundas
Computer Science · Engineering · Mathematics · #33C05 #34A30 #Advanced Numerical Analysis Techniques #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.0811.4641
openalex publication_date 2008/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper classifies algebraic transformations of Gauss hypergeometric functions with the local exponent differences (1/2,1/4,1/4), (1/2,1/3,1/6) and (1/3,1/3,1/3). These form a special class of algebraic transformations of Gauss hypergeometric functions, of arbitrary high degree. The Gauss hypergeometric functions can be identified as elliptic integrals on the genus 1 curves y=x3-x or y=x3-1. Especially interesting are algebraic transformations of the hypergeometric functions into themselves; these transformations come from isogenies of the respective elliptic curves.