References
E. Artin, J. Tate, Class Field Theory, W.A. Benjamin, 1968.
A. Borel, N. Wallach, Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups, Princeton University Press, Princeton, 1980.
W. Casselman, On the representations ofSL 2 (K) related to binary quadratic forms, Amer. Journal of Math. XCIV (1972), 810–834.
D. Degeorge, N. Wallach, Limit Formulas for Multiplicities inL 2 (Γ/G), Annals of Mathematics 107 (1978), 133–150.
W. Duke, R. Howe, J.-S. Li, Estimating Hecke eigenvalues of Siegel modular forms, Duke Math. Journal 67 (1992), 219–240.
R. Endres, Über die Darstellung singulärer Modulformen halbzahligen Gewichts durch Thetareihen, Math. Zeit. 193 (1986), 15–40.
E. Freitag, Singular Modular Forms and Theta Relations, Springer Lecture Notes in Math. 1487 (1991).
U. Görsch, Eine Invariante des Körpers der Siegelschen Modulfunktionen zur Hauptkongruenzgruppe, Diplomarbeit Universität Heidelberg, 1994.
R. Howe, Notes on the oscillator representation, Preprint.
R. Howe, ϑ series and invariant theory, in “Automorphic Forms, Representations, and L-functions”, Proc. Symp. Pure Math. 33, American Math. Soc. Providence (1979), 275–28.
R. Howe, Automorphic forms of low rank, in “Non-commutative Harmonic Analysis”, Springer Lecture Notes in Math. 880 (1980), 211–248.
R. Howe, On a notion of rank for unitary representations of classical groups, In “C.I.M.E. Summer School on Harmonic Analysis” (I. Cortona, ed.) (1980), 223–331.
R. Howe, Small unitary representations of classical groups, in “Group Representations, Ergodic Theory, Operator Algebras and Math. Physics” (C. Moore, ed.), Springer-Verlag, (1986) 121–150.
D. Johnson, J. Millson, Modular Lagrangians and the theta multiplier, Invent. Math. 100 (1990), 143–165.
M. Kneser, Strong approximation, in “Algebraic Groups and Discontinuous Subgroups” (A. Borel, G.D. Mostow, eds.), P.S.P.M. IX, (1966), 187–196.
S. Kudla, Splitting metaplectic covers of dual reductive paris, Israel Journal of Math. 87 (1994), 361–401.
S. Lang, Algebraic Number Theory, 2nd ed. Graduate Texts in Math., Springer-Verlag 110, 1994.
R.P. Langlands, The dimension of spaces of automorphic forms, Amer. J. Math. 85 (1963), 99–125.
J.-S. Li, Automorphic forms with degenerate Fourier coefficients, preprint.
J.-S. Li, Singular unitary representations of classical groups, Inven. Math. 97 (1989), 237–255.
J.-S. Li, J. Millson, On the first Betti number of a hyperbolic manifold with an arithmetic fundamental group, Duke Math. Journal 71 (1993), 365–401.
G. Lion, M. Vergne, The Weil Representation, Maslov Index and Theta Series, Progress in Math. 6, Birkäuser, 1980.
C. Moeglin, M.F. Vigneras, J.L. Waldspurger, Correspondence de Howe sur un corpsp-adique, Springer Lect. Notes in Math. 1291 (1987).
O.T. O'Meara, Introduction to Quadratic Forms, Ergebnisse der Mathematik 68, Springer-Verlag, 1972.
P. Sarnak, Diophantine problems and linear groups, in “Proc. Intl. Cong. Math.” (1991), 459–471.
P. Sarnak, X. Xue, Bounds for multiplicities of automorphic spectrum, Duke Math. Journal 64 (1991), 207–227.
G. Savin, Limit multiplicities of cusp forms, Inven. Math. 95 (1989), 149–159.
J.P. Serre, Corps Locaux, Hermann, Paris, 1968.
J. Tate, Fourier analysis in number fields and Hecke's zeta-functions, in “Algebraic Number Theory” (J.W.S. Cassels, A. Fröhlich, eds.), Academic Press, 1967, 305–347.
D. Vogan, G. Zuckerman, Unitary representations with non-zero cohomology, Compositio Math. 53 (1984), 51–90.
A. Weil, Sur certains groupes d'operateurs unitaires, Acta Math. 111 (1964), 143–211.
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Sloan Fellow. Supported in part by NSF grant No. DMS-9203142
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Li, J.S. On the dimensions of spaces of siegel modular forms of weight one. Geometric and Functional Analysis 6, 512–555 (1996). https://doi.org/10.1007/BF02249262
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DOI: https://doi.org/10.1007/BF02249262