Non-torsion algebraic cycles on the Jacobians of Fermat quotients

We study the Abel-Jacobi image of the Ceresa cycle W₊, ₄-W₊, ₄^-, where W₊, ₄ is the image of the kth symmetric product of a curve X with a base point e on its Jacobian variety. For certain Fermat quotient curves of genus g, we prove that for any choice of the base point and k g-2, the Abel-Jacobi image of the Ceresa cycle is non-torsion. In particular, these cycles are non-torsion modulo rational equivalence.