Stark units in positive characteristic

Abstract

We show that the module of Stark units associated to a sign-normalized rank one Drinfeld module can be obtained from Anderson's equivariant $A$-harmonic series. We apply this to obtain a class formula \`a la Taelman and to prove a several variable log-algebraicity theorem, generalizing Anderson's log-algebraicity theorem. We also give another proof of Anderson's log-algebraicity theorem using shtukas and obtain various results concerning the module of Stark units for Drinfeld modules of arbitrary rank.