  We study the Abel-Jacobi image of the Ceresa cycle W_k-W_k^-, where W_k is
the image of the k-th symmetric product of a curve X on its Jacobian variety.
For the Fermat curve of degree N, we express it in terms of special values of
generalized hypergeometric functions and give a criterion for the non-vanishing
of W_k-W_k^- modulo algebraic equivalence, which is verified numerically for
some N and k.
