Indecomposable Higher Chow cycles on Jacobians
  We construct some natural cycles with trivial regulator in the higher Chow groups of Jacobians. For hyperelliptic curves we use a criterion due to J. Lewis to prove that the cycles we construct are indecomposable, and then use a specialization argument to prove indecomposability for more general curves.   Please note that math.AG/9909062 has become an obsolete version of some of the results in the present paper. 
Alberto Collino and Najmuddin Fakhruddin