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CM Periods, CM Regulators, and Hypergeometric Functions, I

Published online by Cambridge University Press:  20 November 2018

Masanori Asakura  and
Noriyuki Otsubo
Masanori Asakura
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo, 060-0810 Japan email: asakura@math.sci.hokudai.ac.jp
Noriyuki Otsubo
Affiliation:
Department of Mathematics and Informatics, Chiba University, Chiba, 263-8522 Japan email: otsubo@math.s.chiba-u.ac.jp
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Abstract

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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.

Keywords

14D0719F2733C2011G1514K22periodregulatorcomplex multiplicationhypergeometric function
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 70 , Issue 3 , 01 June 2018 , pp. 481 - 514
Copyright
Copyright © Canadian Mathematical Society 2018

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