Hyperbolic manifolds and special values of Dedekind zeta-functions

@article{Zagier1986HyperbolicMA,
  title={Hyperbolic manifolds and special values of Dedekind zeta-functions},
  author={Don Zagier},
  journal={Inventiones mathematicae},
  year={1986},
  volume={83},
  pages={285-301}
}
  • D. Zagier
  • Published 1 June 1986
  • Mathematics
  • Inventiones mathematicae
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References

SHOWING 1-7 OF 7 REFERENCES
The Geometry and Topology of Three-Manifolds (Chapter 7, "Computation of Volume'
  • by J. Milnor). Mimeographed lecture notes,
  • 1979
Hyperbolic Structures on 3-manifolds, I: Deformation of acylindrical manifolds
This is the first in a series of papers showing that Haken manifolds have hyperbolic structures; this first was published, the second two have existed only in preprint form, and later preprints
Commensurability classes and volumes of hyperbolic 3-manifolds
© Scuola Normale Superiore, Pisa, 1981, tous droits réservés. L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze »
Berechnung von Zetafunktionen an ganzzahligen Stellen
Über die Werte der Dedekindschen Zetafunktion