×

Rings of Hilbert modular forms. (English) Zbl 0515.10027


MSC:

11F41 Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
11F06 Structure of modular groups and generalizations; arithmetic groups
14M10 Complete intersections
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
11R11 Quadratic extensions

References:

[1] M.F. Atiyah and I.G. Macdonald : Introduction to Commutative Algebra , Addison-Wesley, Reading, Mass., 1969. · Zbl 0175.03601
[2] Z.I. Borevich and I.R. Shafarevich : Number Theory , Academic Press, New York, 1969. · Zbl 0145.04902
[3] E. Freitag : Lokale und globale invarianten der Hilbertschen modulgruppe , Invent. Math. 17 (1972), 106-134. · Zbl 0272.32010 · doi:10.1007/BF01418935
[4] G. Van Der Geer : Hilbert modular forms for the field Q(\surd 6) , Math. Ann. 233 (1978), 163-179. _ · Zbl 0357.10014 · doi:10.1007/BF01421924
[5] G. Van Der Geer and D. Zagier : The Hilbert modular group for the field Q(\surd 13) , Invent. Math. 42 (1977), 93-133. · Zbl 0366.10024 · doi:10.1007/BF01389785
[6] W. Hammond : The Hilbert modular surface of a real quadratic field , Math. Ann. 200 (1973), 25-45. · Zbl 0236.14014 · doi:10.1007/BF01578290
[7] F. Hirzebruch : Hilbert modular surfaces , L’Enseignement Math. 19 (1974), 182-281. · Zbl 0285.14007
[8] F. Hirzebruch : Hilbert’s modular group for the field Q(\surd 5) and the cubic diagonal surface of Clebsch and Klein , Russian Math. Surveys 31 (1976), 96-110. · Zbl 0356.14010 · doi:10.1070/RM1976v031n05ABEH004190
[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. · Zbl 0369.10017
[10] A. Prestel : Die elliptische Fixpunte der Hilbertschen Modulgruppe , Math. Ann. 117 (1968),181-209. · Zbl 0159.11302 · doi:10.1007/BF01350863
[11] H. Shimizu : On discontinuous groups operating on the product of upper half planes , Ann. of Math. 77 (1963), 33-71. · Zbl 0218.10045 · doi:10.2307/1970201
[12] R.P. Stanley : Invariants of finite groups and their applications to combinatorics , Bull. A.M.S. (new series) 1 (1979), 443-594. · Zbl 0497.20002 · doi:10.1090/S0273-0979-1979-14597-X
[13] R.P. Stanley : Hilbert functions of graded algebras , Advances in Mathematics 28 (1978), 57-83. · Zbl 0384.13012 · doi:10.1016/0001-8708(78)90045-2
[14] E. Thomas and A. Vasquez : Chern numbers of Hilbert modular varieties , J. für r. und ang. Math. 324 (1981), 192-210. · Zbl 0491.14019
[15] M.-F. Vignéras : Invariants numériques des groupes de Hilbert , Math. Ann. 224 (1976), 189-215. · Zbl 0325.12004 · doi:10.1007/BF01459845
[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. · Zbl 0467.10021 · doi:10.1007/BF01450651
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.