Analogs of Δ(z) for triangular Shimura curves

Shujuan Ji

Acta Arithmetica (1998)

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

Abstract

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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.

How to cite

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Shujuan 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

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  1. [Ji] S. Ji, Arithmetic and geometry on triangular Shimura curves, Caltech Ph.D. thesis, 1995. 
  2. S. Lang, Elliptic Functions, Springer, 1987. 
  3. [Sh1] G. Shimura, Construction of class fields and zeta functions of algebraic curves, Ann. of Math. 85 (1967), 58-159. Zbl0204.07201
  4. [Sh2] G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Princeton Univ. Press, 1971. 
  5. [Ta] K. Takeuchi, Arithmetic triangle groups, J. Math. Soc. Japan 29 (1977), 91-106. Zbl0344.20035
  6. [Vi] M.-F. Vignéras, Arithmétique des Algèbres de Quaternions, Springer, 1980. Zbl0422.12008

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