Picard modular surface

In mathematics, a Picard modular surface, studied by Picard (1881), is a complex surface constructed as a quotient of the unit ball in C² by a Picard modular group. Picard modular surfaces are some of the simplest examples of Shimura varieties and are sometimes used as a test case for the general theory of Shimura varieties.

See also

• Hilbert modular surface
• Siegel modular variety

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, doi:10.24033/asens.203