The covolume of quaternion groups on the four-dimensional hyperbolic space

Stefan Breulmann; Volker Helmke

Acta Arithmetica (1996)

  • Volume: 77, Issue: 1, page 9-21
  • ISSN: 0065-1036

How to cite

top

Stefan Breulmann, and Volker Helmke. "The covolume of quaternion groups on the four-dimensional hyperbolic space." Acta Arithmetica 77.1 (1996): 9-21. <http://eudml.org/doc/206911>.

@article{StefanBreulmann1996,
author = {Stefan Breulmann, Volker Helmke},
journal = {Acta Arithmetica},
keywords = {discontinuous groups; volume of fundamental domain; quaternion groups; hyperbolic four-space; linear-fractional transformation; finite covolume; Maaß-Selberg relations; Stokes' theorem; Fourier expansion of Eisenstein series},
language = {eng},
number = {1},
pages = {9-21},
title = {The covolume of quaternion groups on the four-dimensional hyperbolic space},
url = {http://eudml.org/doc/206911},
volume = {77},
year = {1996},
}

TY - JOUR
AU - Stefan Breulmann
AU - Volker Helmke
TI - The covolume of quaternion groups on the four-dimensional hyperbolic space
JO - Acta Arithmetica
PY - 1996
VL - 77
IS - 1
SP - 9
EP - 21
LA - eng
KW - discontinuous groups; volume of fundamental domain; quaternion groups; hyperbolic four-space; linear-fractional transformation; finite covolume; Maaß-Selberg relations; Stokes' theorem; Fourier expansion of Eisenstein series
UR - http://eudml.org/doc/206911
ER -

References

top
  1. [De] M. Deuring, Algebren, 2. Auf., Springer, Berlin, 1968. 
  2. [EGM] J. Elstrodt, F. Grunewald and J. Mennicke, Eisenstein series on three-dimensional hyperbolic space and imaginary quadratic number fields, J. Reine Angew. Math. 360 (1985), 160-213. Zbl0555.10012
  3. [Gr] L. Greenberg, Finiteness theorems for Fuchsian and Kleinian groups, in: Discrete Groups and Automorphic Functions, Proc. Conf. Cambridge 1975, W. J. Harvey (ed.), Academic Press, London, 1977, 199-257. 
  4. [GS] V. A. Gritsenko and R. Schulze-Pillot, Eisenstein series on four-dimensional hyperbolic space, Acta Arith. 67 (1994), 241-268. Zbl0810.11035
  5. [Kr] A. Krieg, Eisenstein-series on real, complex and quaternionic half-spaces, Pacific J. Math. 133 (1988), 315-354. Zbl0657.10025
  6. [Ro] W. Roelcke, Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. II, Math. Ann. 168 (1967), 261-324. 
  7. [Sa] P. Sarnak, The arithmetic and geometry of some hyperbolic three manifolds, Acta Math. 151 (1983), 253-295. Zbl0527.10022
  8. [Wi] N. J. Wielenberg, Discrete Moebius groups: Fundamental polyhedra and convergence, Amer. J. Math. 99 (1977), 861-877. Zbl0373.57024
  9. [Za] D. B. Zagier, Modular forms whose Fourier coefficients involve zeta functions of quadratic fields, in: Lecture Notes in Math. 627, Springer, Berlin, 1977, 105-169. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.