Let C be a curve defined
over a complete discrete valuation subfield of ℂp. Assuming that C has good
reduction over the residue field, we compute the syntomic regulator on a certain part
of K4(3)(C). The result can be expressed in terms of p-adic polylogarithms and
Coleman integration. We also compute the syntomic regulator on a certain part of
K4(3)(F) for the function field F of C. The result can be expressed in terms of p-adic
polylogarithms and Coleman integration, or by using a trilinear map (“triple index”)
on certain functions.