Uniformization of certain Shimura curves
Volume 58 / 2002
Banach Center Publications 58 (2002), 13-26
MSC: Primary 11G18; Secondary 14G35
DOI: 10.4064/bc58-0-1
Abstract
We present an approach to the uniformization of certain Shimura curves by means of automorphic functions, obtained by integration of non-linear differential equations. The method takes as its starting point a differential construction of the modular $j$-function, first worked out by R. Dedekind in 1877, and makes use of a differential operator of the third order, introduced by H. A. Schwarz in 1873.
