On sums of S-integers of bounded norm

@article{Frei2013OnSO,
  title={On sums of S-integers of bounded norm},
  author={Christopher Frei and Robert F. Tichy and Volker Ziegler},
  journal={Monatshefte f{\"u}r Mathematik},
  year={2013},
  volume={175},
  pages={241-247}
}
We prove an asymptotic formula for the number of $$S$$S-integers in a number field $$K$$K that can be represented by a sum of $$n$$n$$S$$S-integers of bounded norm. 
Constrained Triangulations, Volumes of Polytopes, and Unit Equations
TLDR
An equivalent and easy-to-check combinatorial criterion for the facets of $\mathcal{P}$ is proved and this leads to an exact formula for the volume of a polytope arising in the theory of unit equations.
30 years of collaboration
TLDR
This paper focuses on two topics in more detail, namely a problem that origins from a conjecture of Rényi and Erdős (on the number of terms of the square of a polynomial) and another one that originated from a question of Zelinsky ( on the unit sum number problem).

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