References
Ash, A., Mumford, D., Rapoport, M., Tai, Y.: Smooth compactifications of locally symmetric varieties. Brookline, Mass.: Mathematical Sciences Press 1975
Berwick, W.H.H.: Algebraic number fields with two independent units, Proc. London Math. Soc. (2)34, 360–78 (1932)
Cohn, H.: Formal ring of a cubíc solid angle. J. Number Theory10, 135–50 (1978)
Delone, B.N., Faddeev, D.K.: The theory of irrationalities of the third degree. Translations of Mathematical Monographs, Vol. 10. Providence, R.I.: American Mathematical Society 1964
Ehlers, F.: Eine Klasse komplexer Mannigfaltigkeiten und die Auflösung einiger isolierter Singularitäten. Math. Ann.218, 127–56 (1975)
Fujiki, A.: On resolutions of cyclic quotient singularities. Publ. RIMS, Kyoto Univ.10, 293–328 (1974)
Hasse, H.: Arithmetische Bestimmung von Grundeinheit und Klassenzahl in zyklischen kubischen und biquadratischen Zahlkörpern. Math. Abh.3, 289–379 (1975)
Hirzebruch, F.: The Hilbert modular group, resolution of the singularities at the cusps and related problems. Sem. Bourbaki no. 396 1970/71
Hirzebruch, F.: Hilbert Modular surfaces. L'Enseignement Math.19, 183–281 (1974)
Nagell, T.: Zur Arithmetik der Polynome. Abh. Math. Sem. Univ. Hamburg1, 179–194 (1922)
Nakamula, K.: On a fundamental domain forR 3+ . J. Fac. Sci. University of Tokyo, Sect. 1A, Vol. 24 701–13 (1977)
Satake, I.: On the arithmetic of tube domains. Bull. Am. Math. Soc.79, 1076–94 (1973)
Satake, I.: On the blowing-ups of Hilbert modular surfaces. J. Fac. Sci. University of Tokyo, Sect. 1A24, 221–9 (1977)
Shintani, T.: On evaluation of zeta functions of totally real algebraic number fields at non-positive integers. J. Fac. Sci. University of Tokyo, Sect. 1A23, 393–417 (1976)
Stender, H.J.: Einheiten für eine allgemeine Klasse total reeller algebraischer Zahlkörper. J. Reine Angew. Math.257, 151–78 (1972)
Thomas, E.: Fundamental units for orders in certain cubic number fields. J. Reine Angew. Math.310, 33–55 (1979)
Zagier, D.: A Kronecker limit formula for real quadratic fields. Math. Ann.213, 153–184 (1975)
Zagier, D.: Valeurs des fonctions zeta des corps quadratiques reel aux entiers negatifs. Asterisque, no. 41–42, Soc. Math. de France, 1977
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This paper is based upon research supported by grants from the National Science Foundation
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Thomas, E., Vasquez, A.T. On the resolution of cusp singularities and the Shintani decomposition in totally real cubic number fields. Math. Ann. 247, 1–20 (1980). https://doi.org/10.1007/BF01359864
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DOI: https://doi.org/10.1007/BF01359864