References
Berman, S., Moody, R.: Multiplicities in Lie algebras. Proc. Am. Math. Soc. 76 (1979), 223–228
Cohn, H.: Support polygons and the resolution of modular functional singularities. Acta Arith.24, 261–278 (1973)
Feingold, A., Lepowsky, J.: The Weyl-Kac character formula and power series identities. Advances in Math.29, 271–309 (1978)
Garland, H., Lepowsky, J.: Lie algebra homology and the Macdonald-Kac formulas. Invent. Math.34, 37–76 (1976)
Grauert, H., Fritzsche, K.: Several complex variables. Graduate Texts in Mathematics, Vol. 38. Berlin, Heidelberg, New York: Springer 1976
Gundlach, K.-B.: Some new results in the theory of Hilbert's modular group. Contributions to function theory, pp. 165–180. Bombay: Tata Institute 1960
Hirzebruch, F.: The Hilbert modular group, resolution of singularities at the cusps and related problems. Sém. Bourbaki 1970/71, Exposé 396. Lecture Notes in Mathematics, Vol. 244, pp. 275–288. Berlin, Heidelberg, New York: Springer 1971
Hirzebruch, F.: Hilbert modular surfaces. Enseign. Math.19, 183–281 (1973)
Hirzebruch, F.: The ring of Hilbert modular forms for real quadratic fields of small discriminant. Modular function of one variable. VI. Lecture Notes in Mathematics, Vol. 627, pp. 287–323. Berlin, Heidelberg, New York: Springer 1977
Kac, V.: Simple irreducible graded Lie algebras of finite growth (in Russian). Izv. Akad. Nauk. SSSR32, 1323–1367 (1968). English translation: Math. USSR-Izvestija2, 1271–1311 (1968)
Kac, V.: Some properties of contragredient Lie algebras (in Russian). Trudy MIEM5, 48–60 (1969)
Kac, V.: Infinite-dimensional Lie algebras and Dedekind's η-function (in Russian). Funkt. Anal. i Ego Prilozheniya8, 77–78 (1974). English translation: Functional Anal. Appl.8, 68–70 (1974)
Kac, V.: Infinite-dimensional algebras, Dedekind's η-function, classical Möbius function and the very strange formula. Adv. Math.30, 85–136 (1978)
Karras, U.: Eigenschaften der lokalen Ringe in zweidimensionalen Spitzen. Math. Ann.215, 117–129 (1975)
Klein, F.: Ausgewählte Kapitel der Zahlentheorie, Vorlesungen, 1895/96. Leipzig: B.G. Teubner 1907
Moody, R.: A new class of Lie algebras. J. Algebra10, 210–230 (1968)
Moody, R.: Root systems of hyperbolic type. Adv. Math.33, 144–160 (1979)
Siegel, C.: Lectures in advanced analytic number theory. Bombay: Tata Institute 1961, reissued 1965
Author information
Authors and Affiliations
Additional information
During the course of this work, this author was partially supported by a Yale University Junior Faculty Fellowship, a Sloan Foundation Fellowship, and NSF grants MPS 72-05055 AO3 and MCS 78-02439
Supported by a National Research Council of Canada operating grant
Rights and permissions
About this article
Cite this article
Lepowsky, J., Moody, R.V. Hyperbolic Lie algebras and quasi-regular cusps on Hilbert modular surfaces. Math. Ann. 245, 63–88 (1979). https://doi.org/10.1007/BF01420431
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01420431