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CM periods, CM Regulators and Hypergeometric Functions, I

Published:2017-08-03

• Masanori Asakura,
Department of Mathematics, Hokkaido University, Sapporo, 060-0810 Japan
• Noriyuki Otsubo,
Department of Mathematics and Informatics, Chiba University, Chiba, 263-8522 Japan
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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 ${}_3F_2$, and obtain a new example of non-trivial regulators.
 Keywords: period, regulator, complex multiplication, hypergeometric function
 MSC Classifications: 14D07 - Variation of Hodge structures [See also 32G20] 19F27 - Etale cohomology, higher regulators, zeta and $L$-functions [See also 11G40, 11R42, 11S40, 14F20, 14G10] 33C20 - Generalized hypergeometric series, ${}_pF_q$ 11G15 - Complex multiplication and moduli of abelian varieties [See also 14K22] 14K22 - Complex multiplication [See also 11G15]

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