Mathematische Zeitschrift

, Volume 260, Issue 2, pp 265–275 | Cite as

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

  • Yuuki TadokoroEmail author


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).


Harmonic volume Iterated integral Algebraic cycle 

Mathematics Subject Classification (2000)

14H30 14H40 30F30 32G15 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Natural Science EducationKisarazu National College of TechnologyChibaJapan

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