Intersection numbers of cycles on locally symmetric spaces and Fourier coefficients of holomorphic modular forms in several complex variables

 Access to full text

 Full (PDF)

1. [1] A. ASH, Non-square integrable cohomology of arithmetic groups, Duke Math. J., 47 (1980), 435-449. Zbl0446.20023MR82m:22013
2. [2] A. BOREL, Introduction aux groupes arithmétiques, Publications de l'Institut de Mathématiques de l'Université de Strasbourg XV, Hermann, 1969. Zbl0186.33202MR39 #5577
3. [3] A. BOREL, Stable real cohomology of arithmetic groups II, in Collected Papers III, Springer-Verlag, 1983, 650-684. 
4. [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. Zbl0443.22010MR83c:22018
5. [5] J. COGDELL, The Weil representation and cycles on Picard modular surfaces, Preprint, 1982. 
6. [6] M. GAFFNEY, A special Stokes theorem for complete Riemannian manifolds, Ann. of Math. (2) 60 (1954), 140-145. Zbl0055.40301MR15,986d
7. [7] P. GRIFFITHS and J. HARRIS, Principles of algebraic geometry, Wiley, 1978. Zbl0408.14001MR80b:14001
8. [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. Zbl0332.14009MR56 #11909
9. [9] S. KUDLA and J. MILLSON, Harmonic differentials and closed geodesics on a Riemann surface, Invent. Math., 54 (1979), 193-211. Zbl0429.30038MR81a:53041
10. [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. Zbl0506.32013MR82f:32043
11. [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. Zbl0495.10016MR83m:10037
12. [12] S. KUDLA and J. MILLSON, The theta correspondence and harmonic forms, I, Math. Ann., 274 (1986), 353-378. Zbl0594.10020MR88b:11023
13. [13] S. KUDLA and J. MILLSON, The theta correspondence and harmonic forms, II, Math. Ann., 277 (1987), 267-314. Zbl0618.10022MR89b:11041
14. [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. Zbl0652.10021MR90k:11054
15. [15] G. LION and M. VERGNE, The Weil representation, Maslovindex and theta series, Progr. Math., vol. 6, Birkhauser, 1980. Zbl0444.22005MR81j:58075
16. [16] J. MILLSON, Cycles and harmonic forms on locally symmetric spaces, Canad. Math. Bull., 28 (1985), 3-38. Zbl0575.10022MR87b:11038
17. [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. Zbl0681.32024MR90m:32052
18. [18] J. MILLSON, A regularized theta integral and the cohomology of the boundary, in preparation. 
19. [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. Zbl0514.22007
20. [20] Seminaire H. Cartan, 10, Fonctions Automorphes, E.N.S., 1957-1958. 
21. [21] T. SHINTANI, On construction of holomorphic cusp forms of half integral weight, Nagoya Math. J., 58 (1975), 83-126. Zbl0316.10016MR52 #10603
22. [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. Zbl0466.58004MR84m:32046
23. [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. Zbl0506.10024MR85c:11046
24. [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. Zbl0559.10027MR85d:11047
25. [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. Zbl0582.10018MR87c:32038
26. [26] S. P. WANG, Correspondence of modular forms to cycles associated to O(p, q), J. Differential Geom., 22 (1985), 151-223. Zbl0594.10021MR88a:32040
27. [27] A. WEIL, Sur certains groupes d'opérateurs unitaires, Acta. Math., 111 (1964), 143-211. Zbl0203.03305MR29 #2324

1. Stephen S. Kudla, Michael Rapoport, Cycles on Siegel threefolds and derivatives of Eisenstein series
2. Stephen S. Kudla, Derivatives of Eisenstein series and generating functions for arithmetic cycles