Log-Algebraicity of TwistedA-Harmonic Series and Special Values ofL-Series in Characteristicp

AbstractWe find special points in the Carlitz module related, on the one hand, to the values ats=1 of characteristicpDirichletL-function analogues, and on the other hand, to the values at negative integral values ofsof a characteristicpRiemann zeta-function analogue. The special points are constructed with the help of a general theorem asserting the “log-algebraicity” of the “twistedA-harmonic series” associated to a rank one sign-normalized ellipticA-module. Concerning the “special point index” we prove a Kummer-type criterion and raise some Vandiver-type questions