Picard modular group

Not to be confused with Picard group.

In mathematics, a Picard modular group, studied by Picard (1881), is a group of the form SU(J,L), where L is a 3-dimensional lattice over the ring of integers of an imaginary quadratic field and J is a hermitian form on L of signature (2, 1). Picard modular groups act on the unit sphere in C² and the quotient is called a Picard modular surface.

See also

• Fuchsian group
• Kleinian group

References

• Langlands, Robert P.; Ramakrishnan, Dinakar, eds. (1992), The zeta functions of Picard modular surfaces, Montreal, QC: Univ. Montréal, ISBN 978-2-921120-08-1, MR 1155233
• Picard, Émile (1881), "Sur une extension aux fonctions de deux variables du problème de Riemann relatif aux fonctions hypergéométriques", Annales Scientifiques de l'École Normale Supérieure, Série 2, 10: 305–322