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Hilbert modular forms for the field\(\mathbb{Q}(\sqrt 6 )\)

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References

  1. Blumenthal, O.: Über Modulfunktionen von mehreren Veränderlichen. Math. Ann.56, 58 (1903)

    Google Scholar 

  2. Bombieri, E.: Canonical models of surfaces of general type. Publ. Math. I.H.E.S.42, 171–220 (1973)

    Google Scholar 

  3. van der Geer, G.: On Hilbert modular surfaces of principal congruence subgroups. Dissertation, Rijksuniversiteit te Leiden, 1977

  4. van der Geer, G.: On the minimality of Hilbert modular surfaces of congruence subgroups. To appear

  5. van der Geer, G., Van de Ven, A.: On the minimality of certain Hilbert modular surfaces. In “Complex Analysis and Algebraic Geometry”. Iwanami Shoten and Cambridge University Press 1977

  6. van der Geer, G., Zagier, D.: The Hilbert modular group for the field\(\mathbb{Q}(\sqrt {13} )\). Inventiones Math.42, 93–133 (1977)

    Google Scholar 

  7. Gundlach, K.-B.: Die Bestimmung der Funktionen zur Hilbertschen Modulgruppe des Zahlkörpers\(\mathbb{Q}(\sqrt 5 )\). Math. Ann.152, 226–256 (1963)

    Google Scholar 

  8. Gundlach, K.-B.: Die Bestimmung der Funktionen zu einigen Hilbertschen Modulgruppen. J. reine angew. Math.220, 109–153 (1965)

    Google Scholar 

  9. Hammond, W. F.: The two actions of Hilbert's modular group. To appear in American Journal of Math.

  10. Hirzebruch, F.: Hilbert Modular Surfaces. L'Enseignement Math.19, 183–281 (1973)

    Google Scholar 

  11. Hirzebruch, F.: Hilbert's modular group for the field\(\mathbb{Q}(\sqrt 5 )\) and the cubic diagonal surface of Clebsch and Klein. Russian Math. Surveys31, 96–110 (1976); from Uspekki Math. Nauk.31, 133–166 (1976)

    Google Scholar 

  12. Hirzebruch, F.: The ring of Hilbert modular forms for real quadratic fields of small discriminant. In “Modular Functions of one Variable VI”, Springer Lecture Notes 627, pp. 288–322

  13. Hirzebruch, F.: Überlagerungen der projektiven Ebene und Hilbertsche Modulflächen. To appear

  14. Hirzebruch, F., Van de Ven, A.: Hilbert modular surfaces and the classification of algebraic surfaces. Invent. Math.23, 1–29 (1974)

    Google Scholar 

  15. Hirzebruch, F., Zagier, D.: Classification of Hilbert Modular Surfaces. In “Complex Analysis and Algebraic Geometry”. Iwanami Shoten and Cambridge University Press 1977

  16. Horikawa, E.: Algebraic surfaces of general type with smallc 21 , I. Ann. of Math.104, 357–387 (1976)

    Google Scholar 

  17. Svarčman, O. V.: Simply-connectedness of the factor space of the Hilbert modular group (in Russian). Functional Analysis and its Applications8, 99–100 (1974)

    Google Scholar 

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Supported by the Sonderforschungsbereich für Theoretische Mathematik at Bonn University

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van der Geer, G. Hilbert modular forms for the field\(\mathbb{Q}(\sqrt 6 )\) . Math. Ann. 233, 163–179 (1978). https://doi.org/10.1007/BF01421924

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