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CM periods, CM Regulators and Hypergeometric Functions, I

  • 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 period, regulator, complex multiplication, hypergeometric function
MSC Classifications: 14D07, 19F27, 33C20, 11G15, 14K22 show english descriptions Variation of Hodge structures [See also 32G20]
Etale cohomology, higher regulators, zeta and $L$-functions [See also 11G40, 11R42, 11S40, 14F20, 14G10]
Generalized hypergeometric series, ${}_pF_q$
Complex multiplication and moduli of abelian varieties [See also 14K22]
Complex multiplication [See also 11G15]
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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