Sums of units in function fields

@article{Frei2011SumsOU,
  title={Sums of units in function fields},
  author={Christopher Frei},
  journal={Monatshefte f{\"u}r Mathematik},
  year={2011},
  volume={164},
  pages={39-54}
}
  • C. Frei
  • Published 1 September 2011
  • Mathematics
  • Monatshefte für Mathematik
Let R be the ring of S-integers of an algebraic function field (in one variable) over a perfect field, where S is finite and not empty. It is shown that for every positive integer N there exist elements of R that can not be written as a sum of at most N units. Moreover, all quadratic global function fields whose rings of integers are generated by their units are determined. 
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