CM periods, CM regulators and hypergeometric functions, I

2015/03/27 by Masanori Asakura, Asakura, Masanori, Noriyuki Otsubo +1
Mathematics · #14D07 #19F27 #33C20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1503.07962

openalex publication_date 2015/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the H² of certain surfaces with complex multiplication by a cyclotomic field. The periods are written in terms of values of the gamma function and the conjecture of Gross-Deligne is verified. The regulators of certain K₁-elements are written in terms of values of hypergeometric functions ₃F₂, and we prove their non-vanishing.

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