Euclidean minima of totally real number fields: Algorithmic determination

@article{Cerri2007EuclideanMO,
  title={Euclidean minima of totally real number fields: Algorithmic determination},
  author={Jean-Paul Cerri},
  journal={Math. Comput.},
  year={2007},
  volume={76},
  pages={1547-1575}
}
This article deals with determining of the Euclidean minimum M(K) of a totally real number field K of degree n ≥ 2, using techniques from the geometry of numbers. Our improvements of existing algorithms allow us to compute Euclidean minima for fields of degree 2 to 8 and small discriminants, most of which were unknown. Tables are given at the end of this paper. 

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References

Publications referenced by this paper.
Showing 1-9 of 9 references

Euclidean and inhomogeneous spectra of number fields with unit rank greater than 1 , ( to appear in Journal für die Reine und Angewandte Mathematik )

  • J-P. Cerri, F. Lemmermeyer
  • Proceedings Number Theory Eger
  • 2005

Cerri , De l ’ euclidianité de Q „ q 2 + p 2 + √ 2 « et Q “ p 2 + √ 2 ” pour la norme

  • J-P.
  • J . Th . Nombres Bordeaux
  • 2000

Quême, A computer algorithm for finding new Euclidean number fields

  • Q R.
  • J. Th. Nombres Bordeaux
  • 1998

A computer algorithm for finding new Euclidean number fields

  • D. Bernardi, H. Cohen, M. Olivier
  • J . Th . Nombres Bordeaux
  • 1995

The Euclidean algorithm in algebraic number fields

  • F. Lemmermeyer
  • Expositiones Mathematicae
  • 1995

vol

  • W. T. Tutte Graph Theory, Encyclopedia of Mathematics, its Applications
  • 21, Addison-Wesley
  • 1984

Introduction to the geometry of numbers Classics in Mathematics

  • J.W.S. Cassels
  • SpringerVerlag
  • 1971

The inhomogeneous minima of binary quadratic forms , I

  • H. P. F Swinnerton-Deyer
  • Acta Mathematica

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