Pacific Journal of Mathematics

Fundamental domains for the general linear group.

Douglas Grenier

Article information

Pacific J. Math., Volume 132, Number 2 (1988), 293-317.

First available in Project Euclid: 8 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11H55: Quadratic forms (reduction theory, extreme forms, etc.)
Secondary: 11F72: Spectral theory; Selberg trace formula


Grenier, Douglas. Fundamental domains for the general linear group. Pacific J. Math. 132 (1988), no. 2, 293--317.

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  • [1] D. Bump, Automorphic Forms on GL(3,R)9 Lecture Notes in Mathematics 1083, Springer-Verlag, New York, 1984.
  • [2] D. Gordon, D. Grenier, and A. Terras, Hecke operators and the fundmental domain for SL(3, Z), Math. Comp., 48 (1987), 159-178.
  • [3] E. Gottschling, Explizite Bestimmung der Randflaechen des Fundamentalber- eiches der Modulgruppe zweiten Grades,Math. Ann., 138 (1959), 103-124.
  • [4] D. Grenier, Fundamental Domains for Pn/ GLn(Z) and Applications in Number Theory, Ph.D. Thesis, UCSD, 1986.
  • [5] E. Hecke, Mathematische Werke, Vandenhoeck und Ruprecht, Gottingen, 1970.
  • [6] E. Hecke, Lectures on the Theory of Algebraic Numbers, Springer-Verlag, New York, 1981.
  • [7] H. Maass,Siegel's Modular Forms and Dirichlet Series, Lecture Notes in Math- ematics 216, Springer-Verlag, New York, 1971.
  • [8] H. Maass, bereine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichletscher Reihen durch Funktional gleichung,Math. Ann., 121 (1949), 141-183.
  • [9] H. Minkowski,Gesammelte Abhandlungen, Chelsea,New York, 1967.
  • [10] S. Ryskov, The theory ofermite-Minkowski reduction of positive definitequa- draticforms, J. Soviet Math., 6 (1976),651-676.
  • [11] S. Ryskov andE.Baranovskii,Classicalmethods of the theory of latticepackings, Russian Math. Surveys, 34 (1979), 1-68.
  • [12] A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc, 20 (1956),47-87.
  • [13] C. L. Siegel, Gesammelte Abhandlungen, Springer-Verlag, New York, 1979.
  • [14] C. L. Siegel, Lectures on Quadratic Forms, Tata Institute of Fundamental Research, Bombay, 1963.
  • [15] C. L. Siegel, Symplectic Geometry, AcademicPress, New York, 1964.
  • [16] H. Stark, Fourier coefficients of Maass waveforms, in Modular Forms, R. A. Rankin (Ed.), Horwood, Chichester, 1984, pp. 263-269.
  • [17] A. Terras, Harmonic Analysis on Symmetric Spaces and Applications, Vols. I and II,Springer-Verlag, New York, 1985.
  • [18] A Terras, Some simple aspects of the theory of automorphic forms for GL(n.Z), in TheSelberg TraceFormula and Related Topics,D. Hejhal, P. Sarnak,and A. Terras (Eds.), AMS, Providence, 1986.
  • [19] I Satake, On the compactification of the Siegel space, J. Indian Math. Soc, 20 (1956), 259-281.