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Monatshefte für Mathematik

, Volume 175, Issue 2, pp 241–247 | Cite as

On sums of S-integers of bounded norm

  • Christopher Frei
  • Robert Tichy
  • Volker Ziegler
Article

Abstract

We prove an asymptotic formula for the number of \(S\)-integers in a number field \(K\) that can be represented by a sum of \(n\) \(S\)-integers of bounded norm.

Keywords

Unit equations S-integers Algebraic number fields 

Mathematics Subject Classification (1991)

11D45 11N45 

Notes

Acknowledgments

V. Z. was supported by the Austrian Science Fund (FWF) under the project P 24801-N26.

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Copyright information

© Springer-Verlag Wien 2013

Authors and Affiliations

  • Christopher Frei
    • 1
  • Robert Tichy
    • 1
  • Volker Ziegler
    • 2
  1. 1.Institut für Mathematik ATechnische Universität GrazGrazAustria
  2. 2.Johann Radon Institute for Computational and Applied Mathematics (RICAM)Austrian Academy of SciencesLinzAustria

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