Rings of Hilbert modular forms

E. Thomas; A. T. Vasquez

Compositio Mathematica (1983)

  • Volume: 48, Issue: 2, page 139-165
  • ISSN: 0010-437X

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Thomas, E., and Vasquez, A. T.. "Rings of Hilbert modular forms." Compositio Mathematica 48.2 (1983): 139-165. <http://eudml.org/doc/89589>.

@article{Thomas1983,
author = {Thomas, E., Vasquez, A. T.},
journal = {Compositio Mathematica},
keywords = {real quadratic fields; graded ring of Hilbert modular forms; complete intersection ring; principal congruence subgroups; Gorenstein rings},
language = {eng},
number = {2},
pages = {139-165},
publisher = {Martinus Nijhoff Publishers},
title = {Rings of Hilbert modular forms},
url = {http://eudml.org/doc/89589},
volume = {48},
year = {1983},
}

TY - JOUR
AU - Thomas, E.
AU - Vasquez, A. T.
TI - Rings of Hilbert modular forms
JO - Compositio Mathematica
PY - 1983
PB - Martinus Nijhoff Publishers
VL - 48
IS - 2
SP - 139
EP - 165
LA - eng
KW - real quadratic fields; graded ring of Hilbert modular forms; complete intersection ring; principal congruence subgroups; Gorenstein rings
UR - http://eudml.org/doc/89589
ER -

References

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  1. [1] M.F. Atiyah and I.G. Macdonald: Introduction to Commutative Algebra, Addison-Wesley, Reading, Mass., 1969. Zbl0175.03601MR242802
  2. [2] Z.I. Borevich and I.R. Shafarevich: Number Theory, Academic Press, New York, 1969. Zbl0145.04902
  3. [3] E. Freitag: Lokale und globale invarianten der Hilbertschen modulgruppe, Invent. Math.17 (1972), 106-134. Zbl0272.32010MR318063
  4. [4] G. Van Der Geer: Hilbert modular forms for the field Q(√6), Math. Ann. 233 (1978), 163-179. _ Zbl0357.10014
  5. [5] G. Van Der Geer and D. Zagier: The Hilbert modular group for the field Q(√13), Invent. Math.42 (1977), 93-133. Zbl0366.10024
  6. [6] W. Hammond: The Hilbert modular surface of a real quadratic field, Math. Ann.200 (1973), 25-45. Zbl0236.14014MR337989
  7. [7] F. Hirzebruch: Hilbert modular surfaces, L'Enseignement Math.19 (1974), 182-281. Zbl0285.14007MR393045
  8. [8] F. Hirzebruch: Hilbert's modular group for the field Q(√5) and the cubic diagonal surface of Clebsch and Klein, Russian Math. Surveys31 (1976), 96-110. Zbl0356.14010
  9. [9] F. Hirzebruch: The ring of Hilbert modular forms for real quadratic number fields of small discriminant, Lecture Notes in Math. (vol. 627), Springer-Verlag, Berlin, 1977. Zbl0369.10017MR480355
  10. [10] A. Prestel: Die elliptische Fixpunte der Hilbertschen Modulgruppe, Math. Ann. 117 (1968),181-209. Zbl0159.11302MR228439
  11. [11] H. Shimizu: On discontinuous groups operating on the product of upper half planes, Ann. of Math.77 (1963), 33-71. Zbl0218.10045MR145106
  12. [12] R.P. Stanley: Invariants of finite groups and their applications to combinatorics, Bull. A.M.S. (new series) 1 (1979), 443-594. Zbl0497.20002MR526968
  13. [13] R.P. Stanley: Hilbert functions of graded algebras, Advances in Mathematics28 (1978), 57-83. Zbl0384.13012MR485835
  14. [14] E. Thomas and A. Vasquez: Chern numbers of Hilbert modular varieties, J. für r. und ang. Math. 324 (1981), 192-210. Zbl0491.14019MR614525
  15. [15] M.-F. Vignéras: Invariants numériques des groupes de Hilbert, Math. Ann. 224 (1976), 189-215. Zbl0325.12004MR429755
  16. [16] D. Weisser: The arithmetic genus of the Hilbert modular variety and the elliptic fixed points of the Hilbert modular group, Math. Ann.257 (1981), 9-22. Zbl0467.10021MR630643

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