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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Xie, Baohua 2017. Generators of the sister of Euclidean Picard modular groups. Mathematische Zeitschrift, Vol. 286, Issue. 1-2, p. 521.
    Xie, BaoHua Wang, JieYan and Jiang, YuePing 2015. Generators of the Gauss–Picard modular group in three complex dimensions. Pacific Journal of Mathematics, Vol. 273, Issue. 1, p. 197.
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GENERATORS OF THE EISENSTEIN–PICARD MODULAR GROUP IN THREE COMPLEX DIMENSIONS

  • BAOHUA XIE (a1), JIEYAN WANG (a1) and YUEPING JIANG (a1)
Abstract

Little is known about the generators system of the higher dimensional Picard modular groups. In this paper, we prove that the higher dimensional Eisenstein–Picard modular group PU(3, 1;ℤ[ω3]) in three complex dimensions can be generated by four given transformations.

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COPYRIGHT: © Glasgow Mathematical Journal Trust 2013 
References
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1.Falbel, E., Francsics, G., Lax, P. D. and Parker, J. R., Generators of a Picard modular group in two complex dimensions, Proc. Amer. Math. Soc. 139 (2011), 2439–2447.
2.Falbel, E., Francsics, G. and Parker, J. R., The geometry of Gauss–Picard modular group, Math. Ann. 349 (2011), 459–508.
3.Falbel, E. and Parker, J. R., The geometry of the Eisenstein–Picard modular group, Duke Math. J. 131 (2006), 249–289.
4.Francsics, G. and Lax, P., A semi-explicit fundamental domain for a Picard modular group in complex hyperbolic space, Contemp. Math. 238 (2005), 211–226.
5.Francsics, G. and Lax, P., An explicit fundamental domain for the Picard modular group in two complex dimensions, Preprint (2005), pp. 1–25, arXiv:math/0509708.
6.Francsics, G. and Lax, P., Analysis of a Picard modular group, Proc. Natl. Acad. Sci. USA 103 (2006), 11103–11105.
7.Goldman, W. M., Complex hyperbolic geometry (Clarendon, Oxford, 1999).
8.Hardy, G. H. and Wright, E. M., An introduction to the theory of numbers (Clarendon, Oxford, 1954).
9.Holzapfel, R. P., Invariants of arithmetic ball quotient surfaces, Math. Nachr. 103 (1981), 117–153.
10.Parker, J. R., Notes on complex hyperbolic geometry, Preprint (2003).
11.Stewart, I. N. and Tall, D. O., Algebraic number theory (Chapman and Hall Ltd., 1979).
12.Wang, J., Xiao, Y. and Xie, B., Generators of the Eisenstein–Picard modular groups, J. Aust. Math. Soc. 91 (2011), 421–429.
13.Zhao, T., Generators for the Euclidean–Picard modular groups, Tran. Amer. Math. Soc. 364 (2012), 3241–3263.
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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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