Log-algebraicity of twisted A-harmonic series and special values of L-series in characteristic p, by Greg W. Anderson

This paper has appeared in J. Number Theory 60 (1996), no. 1, 165-209, and so the dvi version has been removed. We find special points in the Carlitz module related, on the one hand, to the values at $s=1$ of characteristic $p$ Dirichlet $L$-series analogues, and on the other hand, to the values at negative integral values of $s$ of the 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.

Greg W. Anderson <gwanders@math.umn.edu>