Abstract
Our starting point is a very general question. Let Γ be an arithmetic subgroup of a reductive Lie group G∞. Then the group T acts on the symmetric space X = G∞/K∞ where K∞ ⊂ G∞ is a maximal compact subgroup.
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Bibliography
BOREL, A. Introduction aux groupes arithmetiques, Herman, Paris, (1969)
BOREL, A. Cohomologie de SL n et valeurs des fonctions zeta aux points entiers. (preprint).
BOREL, A. and J.P. SERRE, Corners and arithmetic groups, Comm. Math. Helv., 48, (1973), 436–491
DAMERELL, L-functions of elliptic curves with complex multiplication, I, II, Acta Arithmetica, 17(1970), 287–301, 19 (1971), 311–317
HARDER, G. A Gauss-Bonnet formula for discrete arithmetically defined groups, Ann. Scient. Ec. Norm. Sup. t. 4, (1971), p. 409–455
HARDER, G. Chevalley groups over function fields and automorphic forms, Ann. of Math., vol 100, No 2, (1974), p. 249–306
HARDER, G. Cohomology of SL2(0), Lie groups and their representations, Proc. of the Summer School on Group Repres., I.M. Gelfand ed., A Hilger, London 1975, p. 139–150
HARDER, G. On the cohomology of discrete arithmetically defined groups, Proc. of the Int. Colloquium on Discrete Subgroups of Liegroups and Applications to Moduli, Bombay, 1973, Oxford University Press, 1975, p. 129–160
HARISH-CHANDRA, Automorphic forms on semisimple Lie groups,Springer lecture Notes, 62, 1968
HECKE, E. Gesammelte Werke, Vandenhoeck u. Ruprecht, Göttingen, (1970)
JACQUET, H. Fonctions de Whittaker associées aus groupes de Chevalley, Bull. Soc. Math. France 95, p. 243–309
LANG, S. Algebraic Number Theory. Addison Wesley Publ. company, (1970)
LANGLANDS, R.P. On the functional equation satisfied by Eisenstein series, Springer lecture Notes, 544, (1976)
LANGLANDS, R.P. Euler Products, James K. Whittemore Lectures, Yale University, (1967)
MENDOZA, E. Dissertation (in Preparation)
MILLSON, J.J. On the first Betti number of a constant negatively curved manifold. Ann. of Math., 104, (1976), p. 235–247
RAZAR, M. Values of Dirichlet series at integers in the critical strip. Springer lecture Notes, 627, (1977), p. 1–9
SCHWERMER, J. Sur la cohomologie des sousgroupes de congruence de SL3 (Z), C.R. Acad. Sc. Paris, 283, (1976), p. 817–820
SCHWERMER, J. Eisensteinreihen und die Kohomologie von Kongruenzuntergruppen von SL„ (Z), Dissertation, Bonner Math. Schriften, Nr. 99, Bonn (1977)
SERRE, J.P. Le probleme des groupes de congruence pour SL2, Ann. of Math., 92, (1970), 489–527.
SERRE, J.P. Cohomologie des Groupes Discrets, Prospects in Mathematics, Ann. of Math. Studies, Princeton University Press, 70, (1971), p. 77–16
SHIMURA, G. On the periods of modular forms. Math. Ann., 229, p. 211–221, 1977
SHIMURA, G. On special values of zeta functions associated with cusp forms, Comm. Pure and Appl. Math. 29. 783–804 (1976)
SHIMURA, G. On some arithmetic properties of modular forms of one and several variables, Ann. of Math. 102, (1975), p. 491–515.
SPRINGER, T. Cusp forms for finite groups, Seminar on Algebraic Groups and related finite Groups, IAS, Springer Lecture Notes, 131, 1970 p. 97–120
SWINNERTON-DYER On the conjectures of Birch, Swinnerton-Dyer, and Tate Proceedings of a Conference on Local Fields, Summer School, Driebergen, p. 132–157, Springer 1967.
WEIL, A. Adeles and algebraic groups, Mimeographed Notes, Princeton 1960
WHITTAKER, E.T. and G.N. WATSON, A course of modern analysis, Cambridge University Press, 1963.
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Harder, G. (1981). Period Integrals of Cohomology Classes Which are Represented by Eisenstein Series. In: Automorphic Forms, Representation Theory and Arithmetic. Tata Institute of Fundamental Research Studies in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-00734-1_2
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DOI: https://doi.org/10.1007/978-3-662-00734-1_2
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