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Integer Points in Parallelepipeds

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Part of the Lecture Notes in Mathematics book series (LNM,volume 785)

Abstract

Let K be a compact convex set in En, symmetric about \( \mathop 0\limits_ = \), and suppose that \( \mathop 0\limits_ = \) lies in the interior of K. We call such a set a convex body. Let V(K) denote the volume of K. (By the volume of K we mean the Riemann integral of the characteristic function of K. It can be proved that every convex body has a volume in this sense. Alternatively, the existence of the volume of K may be added as a hypothesis.)

Keywords

  • Linear Form
  • Unit Ball
  • Convex Body
  • Integer Point
  • Symmetric Convex

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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© 1980 Springer-Verlag Berlin Heidelberg

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(1980). Integer Points in Parallelepipeds. In: Diophantine Approximation. Lecture Notes in Mathematics, vol 785. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-38645-2_4

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  • DOI: https://doi.org/10.1007/978-3-540-38645-2_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09762-4

  • Online ISBN: 978-3-540-38645-2

  • eBook Packages: Springer Book Archive