Abstract
The arithmetic of quaternions is recalled from a constructive point of view. A Hecke module is introduced, defined as a free abelian group on right ideal classes of a quaternion order, together with a natural action of Hecke operators. An equivalent construction in terms of Shimura curves is then introduced, and the quaternion construction is applied to the analysis of specific modular and Shimura curves.
Information
Published: 1 January 2001
First available in Project Euclid: 13 September 2018
zbMATH: 1040.11044
MathSciNet: MR1846458
Digital Object Identifier: 10.2969/aspm/03010177
Rights: Copyright © 2001 Mathematical Society of Japan