@article{CM_1986__60_3_323_0, author = {Harris, Michael}, title = {Arithmetic vector bundles and automorphic forms on Shimura varieties, II}, journal = {Compositio Mathematica}, volume = {60}, year = {1986}, pages = {323-378}, mrnumber = {869106}, zbl = {0612.14019}, language = {en}, url = {http://dml.mathdoc.fr/item/CM_1986__60_3_323_0} }
Harris, Michael. Arithmetic vector bundles and automorphic forms on Shimura varieties, II. Compositio Mathematica, Tome 60 (1986) pp. 323-378. http://gdmltest.u-ga.fr/item/CM_1986__60_3_323_0/
[1] Compactification of arithmetic quotients of bounded symmetric domains, Ann. of Math. 84 (1966) 442-528. | MR 216035 | Zbl 0154.08602
and :[5] Travaux de Shimura. Sém. Bourbaki 23 (1970/71) No. 389. | Numdam | MR 498581 | Zbl 0225.14007
:[6] Variétés de Shimura: Interprétation modulaire, et techniques de construction des modèles canoniques. Proc. Symp. Pure Math. XXXIII (1979) Part 2, 247-290. | MR 546620 | Zbl 0437.14012
:[11] Arithmetic and structure of automorphic forms on bounded symmetric domains. Am. J. Math., 105 (1983) 1171-1194; II, Ibid., 1195-1216. | MR 714773 | Zbl 0527.10025
:[12] Eisenstein series on Shimura varieties. Ann. of Math., 119 (1984). | MR 736560 | Zbl 0589.10030
:[13] Arithmetic vector bundles on Shimura varieties, in A utomorphic Forms of Several Variables, Progress in Math. (Boston: Birkhäuser-Verlag) (1984). | MR 763013 | Zbl 0571.10031
:[19] On canonical models of arithmetic quotients of bounded symmetric domains I, II. Ann. of Math. 91 (1970) 144-222; 92 (1970) 528-549. | MR 257031 | Zbl 0237.14010
:[20] On certain reciprocity laws for theta functions and modular forms. Acta Math. 141 (1978) 35-71. | MR 491518 | Zbl 0402.10030
:[21] The arithmetic of automorphic forms with respect to a unitary group. Ann. of Math. 107 (1978) 569-605. | MR 563087 | Zbl 0409.10016
:[23] Automorphic forms and the periods of abelian varieties. J. Math. Soc. Japan 31 (1979) 561-592. | MR 535097 | Zbl 0456.10015
:[24] The arithmetic of certain zeta functions and automorphic forms on orthogonal groups. Ann. of Math. 111 (1980) 313-375. | MR 569074 | Zbl 0438.12003
:[26] Smooth Compactification of Locally Symmetric Varieties, Brookline, Mass.: Math. Sci. Press (1975). | MR 457437 | Zbl 0334.14007
; , , and :[27] Jr.: On the Fourier coefficients of certain Eisenstein series on the adèle group. In: Number Theory, Algebraic Geometry, and Commutative Algebra: in Honor of Y. Akizuki, Tokyo: Kinokuniya (1973). | MR 367320 | Zbl 0283.10017
,[28] Arithmetic of monomial relations between the periods of abelian varieties. Thesis, Princeton University (1981).
:[29] L2-cohomology and intersection cohomology of certain arithmetic varieties. In B. Srinivasan and J. Sally (eds) Emmy Noether in Bryn Mawr. New York: Springer-Verlag (1983) 119-131. | MR 713796 | Zbl 0541.14015
:[30] Groupes Rèductifs. Publ. Math. I.H.E.S. 27 (1965) 55-151. | Numdam | MR 207712 | Zbl 0145.17402
and :[31] "1-motifs" et formes automorphes. In Journées Automorphes, Publ. Math. de l'Univ. Paris VII 15 (1983). | MR 723182 | Zbl 0565.14001
:[32] Compactifications of Siegel Moduli Schemes, Cambridge: Cambridge University Press (1985). | MR 853543 | Zbl 0578.14009
:[33] Limit formulas for multiplicities in L2(Γ\G). Ann. of Math. 107 (1978) 133-150. | Zbl 0397.22007
and :[34] Espaces Hermitiens symétriques, notes from a course at I.H.E.S.
:[35] Les schémas de modules de courbes elliptiques. Lecture Notes in Math 349 (1972) 143-316. | MR 337993 | Zbl 0281.14010
and :[36] Modular curves on arithmetic quotients. Duke Math. J. 49 (1982) 633-654. | MR 672500 | Zbl 0501.10025
:[37] Special values of zeta functions attached to Siegel modular forms. Ann. Sci. de l'E.N.S. 14 (1981) 77-120. | Numdam | MR 618732 | Zbl 0465.10022
:[38] Maass operators and Eisenstein series. Math. Ann. 258 (1981) 135-144. | MR 641820 | Zbl 0455.10018
:[39] Fourier coefficients of non-holomorphic Eisenstein series on a tube domain associated to an orthogonal group, to appear.
:[40] Restrictions and expansions of holomorphic representations, J. Fun. Analysis 34, (1979) 29-53. | MR 551108 | Zbl 0433.22011
and :[41] p-adic L-functions for CM fields. Inv. Math. 59 (1978) 199-297. | MR 513095 | Zbl 0417.12003
:[42] On certain arithmetic automorphic forms for SU(1, q). Inv. Math. 52 (1979) 1-26. | MR 532744 | Zbl 0408.10016
:[43] Siegel's Modular Forms and Dirichlet Series, Lecture Notes in Math., 216 (1971). | Zbl 0224.10028
:[44] On the equations defining abelian varieties: I, II, III, Inv. Math. 1 (1966) 287-354; 3 (1967) 75-135, 215-244. | MR 204427 | Zbl 0219.14024
:[45] On modular forms associated with indefinite quadratic forms of signature (2, n - 2), Math. Ann. 231 (1977) 97-144. | MR 466026 | Zbl 0346.10013
:[46] Hodge structures of Shimura varieties attached to the unit groups of quaternion algebras, in Advanced Studies in Pare Mathematics 2: Galois Groups and Their Representations, 15-36 Tokyo: Kinokuniya Press (1983). | MR 732459 | Zbl 0594.14003
:[47] Geometry of Classical Domains and the Theory of Automorphic Functions, New York, Gordon and Breach (1969).
:[48] L-functions for the classical groups, notes on a seminar at I.A.S. prepared by (1984).
and :[49] Algebraic Structures of Symmetric Domains, Princeton University Press (1980). | MR 591460 | Zbl 0483.32017
:[50] On a conjecture of Langlands. Ann. of Math. 93 (1971) 1-42. | MR 286942 | Zbl 0291.43013
:[51] Dissertation, Berlin (1901).
:[52] Modules des variétés abéliennes polarisées et fonctions modulaires: I, II, III, In Sém. Cartan 1957/58, exposés 18-20, New York: Benjamin (1967). | Numdam
:[53] On some arithmetic properties of modular forms of one and several variables. Ann. of Math. 102 (1975) 491-515. | MR 491519 | Zbl 0327.10028
:[54] On the Fourier coefficients of modular forms of several variables. Göttinger Nachr. Akad. Wiss. Nr. 17 (1975) 261-268. | MR 485706 | Zbl 0332.32024
:[55] The special values of the zeta functions associated with cusp forms. Comm. Pure Appl. Math. 29 (1976) 783-804. | MR 434962 | Zbl 0348.10015
:[56] On certain zeta functions attached to two Hilbert modular forms: I, II. Ann. of Math. 114 (1981) 127-164, 569-607. | Zbl 0486.10021
:[57] Arithmetic of differential operators on symmetric domains. Duke Math. J. 48 (1981) 813-843. | MR 782579 | Zbl 0487.10021
:[58] Algebraic relations between critical values of zeta functions and inner products. Am. J. Math. 105 (1983) 253-285. | MR 692113 | Zbl 0518.10032
:[59] On Eisenstein series, Duke Math. J. 50 (1983) 417-476. | MR 705034 | Zbl 0519.10019
:[60] The rationality of the Fourier coefficients of certain Eisenstein series on tube domains. Compositio Math. 32 (1976) 225-291. | Numdam | MR 419367 | Zbl 0346.10014
:[61] Analytic continuation of holomorphic discrete series. A cta Math. 136 (1976) 1-59. | MR 480883 | Zbl 0356.32020
and :[62] Analytic continuation of the discrete series II. Trans. A.M.S. 251 (1979) 19-37. | MR 531967 | Zbl 0419.22018
:[63] Sur les coefficients de Fourier des formes modulaires de poids demi-en-tier. J. Math. pures et appl. 60 (1981) 375-484. | MR 646366 | Zbl 0431.10015
:[64] Correspondances de Shimura et quaternions, preprint (1983). | MR 1103429 | Zbl 0724.11026
:[65] Fine structure of Hermitian symmetric spaces. In: Symmetric Spaces Short Lectures, pp. 271-357, New York: Dekker (1972). | MR 404716 | Zbl 0257.32014
:[66] Generalized Cayley transformations of bounded symmetric domains. Am. J. Math. 87 (1965) 899-939. | MR 192002 | Zbl 0137.27403
and :[67] L2-cohomology of warped products and arithmetic groups. Inv. Math. 70 (1982) 169-218. | MR 684171 | Zbl 0508.20020
:[68] L2-cohomology and intersection homology of locally symmetric varieties, II, preprint (1983). | Zbl 0624.14014
:[69] Théorie de Hodge, II, Publ. Math. I.H.E.S. 40 (1971) 5-58. | Numdam | MR 498551 | Zbl 0219.14007
:[70] On limit multiplicities of discrete series representations in spaces of automorphic forms Inv. Math. 83 (1986) 265-284. | MR 818353 | Zbl 0582.22012
:[71] Arithmetische Kompaktifizierung des Modulraums der abelschen Varietäten. In Arbeitstagung Bonn 1984, Lect. Notes in Math. 1111 (1985) 321-383. | MR 797429 | Zbl 0597.14036
:[72] Arithmetic vector bundles and automorphic forms on Shimura varieties, I. Inv. Math. 82 (1985) 151-189. | MR 808114 | Zbl 0598.14019
:[73] Automorphic forms of discrete type as coherent cohomology classes (preprint). | MR 492234
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