# Analogs of Δ(z) for triangular Shimura curves

Acta Arithmetica (1998)

- Volume: 84, Issue: 2, page 97-108
- ISSN: 0065-1036

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topShujuan Ji. "Analogs of Δ(z) for triangular Shimura curves." Acta Arithmetica 84.2 (1998): 97-108. <http://eudml.org/doc/207142>.

@article{ShujuanJi1998,

abstract = {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.},

author = {Shujuan Ji},

journal = {Acta Arithmetica},

keywords = {triangular Shimura curves; modular groups; discriminant; cocompact arithmetic triangle groups; automorphic function},

language = {eng},

number = {2},

pages = {97-108},

title = {Analogs of Δ(z) for triangular Shimura curves},

url = {http://eudml.org/doc/207142},

volume = {84},

year = {1998},

}

TY - JOUR

AU - Shujuan Ji

TI - Analogs of Δ(z) for triangular Shimura curves

JO - Acta Arithmetica

PY - 1998

VL - 84

IS - 2

SP - 97

EP - 108

AB - 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.

LA - eng

KW - triangular Shimura curves; modular groups; discriminant; cocompact arithmetic triangle groups; automorphic function

UR - http://eudml.org/doc/207142

ER -

## References

top- [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. Zbl0204.07201
- [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. Zbl0344.20035
- [Vi] M.-F. Vignéras, Arithmétique des Algèbres de Quaternions, Springer, 1980. Zbl0422.12008

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