  In this paper we study the group K_{2n}^{(n+1)}(F) where F is the function
field of a complete, smooth, geometrically irreducible curve C over a number
field, assuming the Beilinson--Soul\'e conjecture on weights. In particular, we
compute the Beilinson regulator on a subgroup of K_{2n}^{(n+1)}(F), using the
complexes constructed in previous work by the author. We study the boundary map
in the localization sequence for n = 3 (the case n = 2 was done in a previous
paper). We combine our results with some results of Goncharov in order to
obtain a complete description of the image of the regulator map on K_4^{(3)}(C)
and K_6^{(4)}(C), independent of any conjectures.
