Log-algebraicity of twisted A-harmonic series and special values of L-series in characteristic p

We find special points in the Carlitz module related, on the one hand, to the values at s = 1 of characteristic p Dirichlet L-function analogues, and on the other hand, to the values at negative integral values of s of a characteristic p Riemann zeta-function analogue. The special points are constructed with the help of a general theorem asserting the "log-algebraicity" of the "twisted A-harmonic series" associated to a rank one sign-normalized elliptic A-module. Concerning the "special point index" we prove a Kummer-type criterion and raise some Vandiver-type questions.