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References
[B]A. Borel, Cohomolgie de sous-groupes discretes et representations de groupes semi-simples, Asterisque 32–33 (1976).
[DW]D. DeGeorge and N. Wallach, Limit formulas for multiplicities inL 2 (G/г), I, Ann. of Math. 107 (1978); II, Ann. of Math. 129 (1978).
[HW]R. Hotta and N. Wallach, On Matsushima's formula for the Betti numbers of a locally symmetric space, Osaka J. Math. 12 (1975).
[K]D. Kazhdan, Some applications of Weil representation. J. D'Analyse Math. 32 (1977).
[Kn]M. Kneser, Strong approximation, Proc. Sympos. Pure Math. 9 (1966).
[L]J. Li, Non-vanishing Theorems for the cohomology of certain arithmetic quotients, Preprint.
[Ma]Y. Matsushima, On the first Betti number of compact quotient spaces of higher-dimensional symmetric spaces, Ann. of Math. 2 (1962), 75.
[M]J. Millson, On the first Betti number of a constant negatively curved manifold, Ann. of Math. 104 (1976).
[MR]J. Millson and M. Raghunathan, Geometric construction of cohomology for arithmetic groups, Proc. Indian Acad. Sci. (Math. Sci.) 90 (1981).
[S]P. Sarnak, Betti Numbers of congruence groups, Preprint.
[SX]P. Sarnak and X. Xue, Bounds for multiplicities of automorphic forms, Duke Math. J. 64, 1991.
[X]X. Xue, On the first Betti numbers of hyperbolic surfaces, Duke Math. J. 64, 1991.
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Xue, X. On the Betti numbers of a hyperbolic manifold. Geometric and Functional Analysis 2, 126–136 (1992). https://doi.org/10.1007/BF01895709
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DOI: https://doi.org/10.1007/BF01895709