A nontrivial algebraic cycle in the Jacobian variety of the Klein quartic
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 3F2. 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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