Intersection numbers of cycles on locally symmetric spaces and Fourier coefficients of holomorphic modular forms in several complex variables
Publications Mathématiques de l'IHÉS, Tome 71 (1990), pp. 121-172.
@article{PMIHES_1990__71__121_0,
     author = {Kudla, Stephen S. and Millson, John J.},
     title = {Intersection numbers of cycles on locally symmetric spaces and {Fourier} coefficients of holomorphic modular forms in several complex variables},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {121--172},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {71},
     year = {1990},
     zbl = {0722.11026},
     mrnumber = {92e:11035},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_1990__71__121_0/}
}
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Kudla, Stephen S.; Millson, John J. Intersection numbers of cycles on locally symmetric spaces and Fourier coefficients of holomorphic modular forms in several complex variables. Publications Mathématiques de l'IHÉS, Tome 71 (1990), pp. 121-172. http://www.numdam.org/item/PMIHES_1990__71__121_0/

[1] A. Ash, Non-square integrable cohomology of arithmetic groups, Duke Math. J., 47 (1980), 435-449. | MR 82m:22013 | Zbl 0446.20023

[2] A. Borel, Introduction aux groupes arithmétiques, Publications de l'Institut de Mathématiques de l'Université de Strasbourg XV, Hermann, 1969. | MR 39 #5577 | Zbl 0186.33202

[3] A. Borel, Stable real cohomology of arithmetic groups II, in Collected Papers III, Springer-Verlag, 1983, 650-684.

[4] A. Borel and N. Wallach, Continuous cohomology, discrete groups and representations of reductive groups, Ann. of Math. Stud., vol. 94, Princeton Univ. Press, Princeton, N. J., 1980. | MR 83c:22018 | Zbl 0443.22010

[5] J. Cogdell, The Weil representation and cycles on Picard modular surfaces, Preprint, 1982.

[6] M. Gaffney, A special Stokes theorem for complete Riemannian manifolds, Ann. of Math. (2) 60 (1954), 140-145. | MR 15,986d | Zbl 0055.40301

[7] P. Griffiths and J. Harris, Principles of algebraic geometry, Wiley, 1978. | MR 80b:14001 | Zbl 0408.14001

[8] F. Hirzebruch and D. Zagier, Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus, Invent. Math., 36 (1976), 57-113. | EuDML 142414 | MR 56 #11909 | Zbl 0332.14009

[9] S. Kudla and J. Millson, Harmonic differentials and closed geodesics on a Riemann surface, Invent. Math., 54 (1979), 193-211. | EuDML 142678 | MR 81a:53041 | Zbl 0429.30038

[10] S. Kudla and J. Millson, The Poincaré dual of a geodesic algebraic curve in a quotient of the 2-ball, Canad. J. Math., 33 (1979), 485-499. | MR 82f:32043 | Zbl 0506.32013

[11] S. Kudla and J. Millson, Geodesic cycles and the Weil representation, I. Quotients of hyperbolic space and Siegel modular forms, Compos. Math., 45 (1982), 207-217. | Numdam | MR 83m:10037 | Zbl 0495.10016

[12] S. Kudla and J. Millson, The theta correspondence and harmonic forms, I, Math. Ann., 274 (1986), 353-378. | MR 88b:11023 | Zbl 0594.10020

[13] S. Kudla and J. Millson, The theta correspondence and harmonic forms, II, Math. Ann., 277 (1987), 267-314. | MR 89b:11041 | Zbl 0618.10022

[14] S. Kudla and J. Millson, Tubes, cohomology with growth conditions and an application to the theta correspondence, Canad. J. Math., 40 (1988), 1-37. | MR 90k:11054 | Zbl 0652.10021

[15] G. Lion and M. Vergne, The Weil representation, Maslovindex and theta series, Progr. Math., vol. 6, Birkhauser, 1980. | MR 81j:58075 | Zbl 0444.22005

[16] J. Millson, Cycles and harmonic forms on locally symmetric spaces, Canad. Math. Bull., 28 (1985), 3-38. | MR 87b:11038 | Zbl 0575.10022

[17] J. Millson, Intersection numbers of cycles and Fourier coefficients of holomorphic modular forms in several complex variables, Proceedings of Symposia in Pure Math., 41 (1989), Part 2, 129-142. | MR 90m:32052 | Zbl 0681.32024

[18] J. Millson, A regularized theta integral and the cohomology of the boundary, in preparation.

[19] J. Millson and M. S. Raghunathan, Geometric construction of cohomology for arithmetic groups, I, in Geometry and Analysis (Papers dedicated to the Memory of V. K. Patodi), The Indian Academy of Sciences, 1979, 103-123. | Zbl 0514.22007

[20] Seminaire H. Cartan, 10, Fonctions Automorphes, E.N.S., 1957-1958.

[21] T. Shintani, On construction of holomorphic cusp forms of half integral weight, Nagoya Math. J., 58 (1975), 83-126. | MR 52 #10603 | Zbl 0316.10016

[22] Y. L. Tong and S. P. Wang, Harmonic forms dual to geodesic cycles in quotients of SU(p, q), Math. Ann., 258 (1982), 298-318. | MR 84m:32046 | Zbl 0466.58004

[23] Y. L. Tong and S. P. Wang, Theta functions defined by geodesic cycles in quotients of SU(p, 1), Invent. Math., 71 (1983), 467-499. | MR 85c:11046 | Zbl 0506.10024

[24] Y. L. Tong and S. P. Wang, Correspondence of Hermitian modular forms to cycles associated to SU(p, 2), J. Differential Geom., 18 (1983), 163-207. | MR 85d:11047 | Zbl 0559.10027

[25] Y. L. Tong and S. P. Wang, Period integrals in non-compact quotients of SU(p, 1), Duke Math. J., 52 (1985), 649-688. | MR 87c:32038 | Zbl 0582.10018

[26] S. P. Wang, Correspondence of modular forms to cycles associated to O(p, q), J. Differential Geom., 22 (1985), 151-223. | MR 88a:32040 | Zbl 0594.10021

[27] A. Weil, Sur certains groupes d'opérateurs unitaires, Acta. Math., 111 (1964), 143-211. | MR 29 #2324 | Zbl 0203.03305