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On cliques of exceptional units and Lenstra's construction of Euclidean fields

Part of the Lecture Notes in Mathematics book series (LNM,volume 1380)

Abstract

In the wake of a method for detecting Euclidean number fields with the aid of exceptional units, described in 1977 by H. W. Lenstra jr., we study a group action on cliques of exceptional units, determine the corresponding group and exploit the action in some concrete rings. This has also yielded 37 new Euclidean fields in degrees 5, 6, 7, 8, 9, and 10.

AMS subject classification

  • 13F07
  • 11R27
  • 05C25
  • 20B25
  • Euclidean number fields
  • unit equation
  • arithmetic graphs
  • symmetric groups

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© 1989 Springer-Verlag

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Leutbecher, A., Niklasch, G. (1989). On cliques of exceptional units and Lenstra's construction of Euclidean fields. In: Schlickewei, H.P., Wirsing, E. (eds) Number Theory. Lecture Notes in Mathematics, vol 1380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086551

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  • DOI: https://doi.org/10.1007/BFb0086551

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