CM Periods, CM Regulators, and Hypergeometric Functions, I. (1st June 2018)

• Record Type: Journal Article
• Authors: Asakura, Masanori; Otsubo, Noriyuki
• Is Part Of: Canadian journal of mathematics. Volume 70:Number 3(2018)
• Page Start: 481
• Page End: 514
• Publication Date: 2018-06-01
• Subjects: 14D07 -- 19F27 -- 33C20 -- 11G15 -- 14K22; period -- regulator -- complex multiplication -- hypergeometric function; Mathematics -- Periodicals; Mathematics; Electronic journals; Periodicals; 510
• DOI: 10.4153/CJM-2017-008-6
• Languages: English
• ISSNs: 0008-414X

Abstract

Abstract: We prove the Gross–Deligne conjecture on CM periods for motives associated with ${{H}^{2}}$ of certain surfaces fibered over the projective line. Then we prove for the same motives a formula which expresses the ${{K}_{1}}$ -regulators in terms of hypergeometric functions $_{3}{{F}_{2}}$, and obtain a new example of non-trivial regulators.