Sums of units in function fields

Abstract

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.

18 pages

Cited by in corpus (3)

• On rings of integers generated by their units
• Additive unit representations in global fields - A survey
• Sums of units in function fields II - The extension problem