Analogs of Δ(z) for triangular Shimura curves

• Autorzy: Shujuan Ji
• Języki publikacji: EN

Abstrakty

EN

We construct analogs of the classical Δ-function for quotients of the upper half plane 𝓗 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.

Kategorie tematyczne

• 11F06: Structure of modular groups and generalizations; arithmetic groups
• 11F12: Automorphic forms, one variable
• 11F03: Modular and automorphic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998
• Tom: 84
• Numer: 2
• Strony: 97-108

Daty

wydano

1998

otrzymano

1996-10-01

Twórcy

autor

Shujuan Ji

• Department of Mathematics, Columbia University, New York, New York 10027, U.S.A.

Bibliografia

• [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.