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The fixed points of the symmetric Hilbert modular group of a real quadratic field with arbitrary discriminant. (English) Zbl 0467.10020


MSC:

11F41 Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
14J20 Arithmetic ground fields for surfaces or higher-dimensional varieties
14H45 Special algebraic curves and curves of low genus
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References:

[1] Hausmann, W.: Kurven auf Hilbertschen Modulflächen. Bonn. Math. Schr.123 (1980) · Zbl 0458.10025
[2] Hirzebruch, F.: Hilbert modular surfaces. Ens. Math.19, 183-281 (1973) · Zbl 0285.14007
[3] Hirzebruch, F., Zagier, D.: Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus. Invent. Math.36, 57-113 (1976) · Zbl 0332.14009 · doi:10.1007/BF01390005
[4] Hirzebruch, F., Zagier, D.: Classification of Hilbert modular surfaces. In: Complex analysis and algebraic geometry, pp. 43-77. Tokyo: Shoten and Cambridge: Cambridge University Press 1977 · Zbl 0354.14011
[5] Karras, U.: Eigenschaften der lokalen Ringe in zweidimensionalen Spitzen. Math. Ann.215, 117-129 (1975) · Zbl 0286.14003 · doi:10.1007/BF01432690
[6] Koll, F.J.: Die elliptischen Fixpunkte und die Spitzen der diskreten Erweiterungen der Hilbertschen Modulgruppe. Bonn. Math. Schr.84 (1976) · Zbl 0347.10023
[7] Prestel, A.: Die elliptischen Fixpunkte der Hilbertschen Modulgruppen. Math. Ann.177, 181-209 (1968) · Zbl 0159.11302 · doi:10.1007/BF01350863
[8] Prestel, A.: Die Fixpunkte der symmetrischen Hilbertschen Modulgruppe zu einem reell quadratischen Zahlkörper mit Primzahldiskriminante. Math. Ann.200, 123-139 (1973) · Zbl 0234.10019 · doi:10.1007/BF01435452
[9] Rohlfs, J.: Arithmetische definierte Gruppen mit Galoisoperation. Invent. Math.48, 185-205 (1978) · Zbl 0391.14007 · doi:10.1007/BF01390250
[10] Shimizu, H.: On discontinuous groups operating on the product of the upper half planes. Ann. Math.77, 33-71 (1963) · Zbl 0218.10045 · doi:10.2307/1970201
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