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 ${}_3{F}_2$. This result tells us the algebraic cycle $C-C^{-}$ is not algebraically equivalent to zero in the Jacobian variety $J(C)$.

arXiv comment8 pages, 1 figure