ON A PHENOMENON DISCOVERED BY HEINZ HELLING

Rehmann U, Vinberg E (2017)
Transformation Groups 22(1): 259-265.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Rehmann, UlfUniBi; Vinberg, E.
Abstract / Bemerkung
The hyperbolic 3-manifolds fibered over the circle with fiber a once punctured torus are considered. Surprisingly, in all of about 200 cases, where the class numbers of their trace fields were calculated, they turned out to be equal to one. This is a report on the work of our friend Heinz Helling during the last several years. Unfortunately, for health problems he is unable to write about it himself. All the main ideas and results presented in this paper belong to him, but some technical details may be different. In a series of preprints [1], [3], [4], [5], H. Helling with co-authors studied some class of hyperbolic 3-manifolds fibered over the circle, and calculated the trace fields of these manifolds. Ten years later he came to the idea to investigate arithmetic properties of these fields. This led him to a surprising result: in all the cases, when he managed to calculate the class number (with the help of a computer program), it turned out to be equal to one!
Erscheinungsjahr
2017
Zeitschriftentitel
Transformation Groups
Band
22
Ausgabe
1
Seite(n)
259-265
ISSN
1083-4362
eISSN
1531-586X
Page URI
https://pub.uni-bielefeld.de/record/2914001

Zitieren

Rehmann U, Vinberg E. ON A PHENOMENON DISCOVERED BY HEINZ HELLING. Transformation Groups. 2017;22(1):259-265.
Rehmann, U., & Vinberg, E. (2017). ON A PHENOMENON DISCOVERED BY HEINZ HELLING. Transformation Groups, 22(1), 259-265. doi:10.1007/s00031-017-9416-y
Rehmann, U., and Vinberg, E. (2017). ON A PHENOMENON DISCOVERED BY HEINZ HELLING. Transformation Groups 22, 259-265.
Rehmann, U., & Vinberg, E., 2017. ON A PHENOMENON DISCOVERED BY HEINZ HELLING. Transformation Groups, 22(1), p 259-265.
U. Rehmann and E. Vinberg, “ON A PHENOMENON DISCOVERED BY HEINZ HELLING”, Transformation Groups, vol. 22, 2017, pp. 259-265.
Rehmann, U., Vinberg, E.: ON A PHENOMENON DISCOVERED BY HEINZ HELLING. Transformation Groups. 22, 259-265 (2017).
Rehmann, Ulf, and Vinberg, E. “ON A PHENOMENON DISCOVERED BY HEINZ HELLING”. Transformation Groups 22.1 (2017): 259-265.

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