Gábor Francsics, Peter D. Lax
A Fundamental Domain for the Picard Modular Group in C$^2$
Preprint series: ESI preprints

MSC:

22E40 Discrete subgroups of Lie groups, See also {20Hxx, 32Nxx}

32M05 Complex Lie groups, automorphism groups of complex spaces, See also {22E10}

Abstract: Our main goal in this paper is to construct a semi-explicit fundamental domain
of the Picard modular group in ${\bf C}^{2}$ that has all the geometric properties
needed for the spectral analysis of the corresponding automorphic
Laplace-Beltrami operator.
Keywords: Fundamental domain, Picard modular group, complex hyperbolic space