ArticleOriginal scientific text
Title
Analogs of Δ(z) for triangular Shimura curves
Authors 1
Affiliations
- Department of Mathematics, Columbia University, New York, New York 10027, U.S.A.
Abstract
We construct analogs of the classical Δ-function for quotients of the upper half plane by certain arithmetic triangle groups Γ coming from quaternion division algebras B. We also establish a relative integrality result concerning modular functions of the form Δ(αz)/Δ(z) for α in B⁺. We give two explicit examples at the end.
Bibliography
- [Ji] S. Ji, Arithmetic and geometry on triangular Shimura curves, Caltech Ph.D. thesis, 1995.
- S. Lang, Elliptic Functions, Springer, 1987.
- [Sh1] G. Shimura, Construction of class fields and zeta functions of algebraic curves, Ann. of Math. 85 (1967), 58-159.
- [Sh2] G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Princeton Univ. Press, 1971.
- [Ta] K. Takeuchi, Arithmetic triangle groups, J. Math. Soc. Japan 29 (1977), 91-106.
- [Vi] M.-F. Vignéras, Arithmétique des Algèbres de Quaternions, Springer, 1980.
Pages:
97-108
Main language of publication
English
Received
1996-10-01
Published
1998
Exact and natural sciences