Solutions of a Linear Equation in a Subgroup of Units in a Function   Field
  Over a large class of function fields, we show that the solutions of some linear equations in the topological closure of a certain subgroup of the group of units in the function field are exactly the solutions that are already in the subgroup. This result solves some cases of the function field analog of an old conjecture proposed by Skolem. 
Chia-Liang Sun
math.NT