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A nontrivial algebraic cycle in the Jacobian variety of the Klein quartic

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Abstract

We prove some value of the harmonic volume for the Klein quartic C is nonzero modulo \(\frac{1}{2}{\mathbb{Z}}\) , using special values of the generalized hypergeometric function 3 F 2. This result tells us the algebraic cycle C − C − is not algebraically equivalent to zero in the Jacobian variety J(C).

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  1. Natural Science Education, Kisarazu National College of Technology, 2-11-1 Kiyomidai-Higashi, Kisarazu, Chiba, 292-0041, Japan

    Yuuki Tadokoro

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  1. Yuuki Tadokoro
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Correspondence to Yuuki Tadokoro.

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Tadokoro, Y. A nontrivial algebraic cycle in the Jacobian variety of the Klein quartic. Math. Z. 260, 265–275 (2008). https://doi.org/10.1007/s00209-007-0273-6

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  • DOI: https://doi.org/10.1007/s00209-007-0273-6

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