An algebro-geometric study of special values of hypergeometric functions ₃F₂

2016/03/15 by Masanori Asakura, Asakura, Masanori, Noriyuki Otsubo +3
Computer Science · Mathematics · #11G15 #14D07 #14K22 (secondary) #19F27 #33C20 (primary) #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1603.04558

openalex publication_date 2016/03/15 · openalex created_date 2018/04/13 · openalex updated_date 2026/07/28

Abstract

For certain class of hypergeometric functions ₃F₂ with rational parameters, we give a sufficient condition for the special value at 1 to be expressed in terms of logarithms of algebraic numbers. We give two proofs, both of which are algebro-geometric and related to higher regulators.

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