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

Yuuki Tadokoro
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Abstract

We prove some value of the harmonic volume for the Klein quartic $C$ is nonzero modulo ${1/2}\{mathbb Z}$, using special values of the generalized hypergeometric function ${}_3F_2$. 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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Yuuki Tadokoro. 2005-08-23. A nontrivial algebraic cycle in the Jacobian variety of the Klein quartic. https://arxiv.org/abs/math/0508433

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