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CM periods, CM regulators and hypergeometric functions, II

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Abstract

We study periods and regulators of a certain class of fibrations of varieties whose relative \(H^1\) has multiplication by a number field. Both are written in terms of values of hypergeometric functions \({}_3F_2\) and the former reduces to values of the \(\Gamma \)-function, which provides examples of the conjecture of Gross–Deligne.

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Acknowledgements

The authors are grateful to the referee for reading the paper very carefully.

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Authors and Affiliations

  1. Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan

    Masanori Asakura

  2. Department of Mathematics and Informatics, Chiba University, Chiba, 263-8522, Japan

    Noriyuki Otsubo

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  1. Masanori Asakura
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  2. Noriyuki Otsubo
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Correspondence to Noriyuki Otsubo.

Additional information

This work is supported by JSPS Grant-in-Aid for Scientific Research, 24540001 and 25400007.

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Asakura, M., Otsubo, N. CM periods, CM regulators and hypergeometric functions, II. Math. Z. 289, 1325–1355 (2018). https://doi.org/10.1007/s00209-017-2001-1

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  • DOI: https://doi.org/10.1007/s00209-017-2001-1

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