Mathematische Annalen

, Volume 274, Issue 3, pp 353–378 | Cite as

The theta correspondence and harmonic forms. I

  • Stephen S. Kudla
  • John J. Millson


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  1. 1.
    Borel, A., Wallach, N.: Continuous cohomology, discrete subgroups and representations of reductive groups. Ann. Math. Stud.94 (1980)Google Scholar
  2. 2.
    Cogdell, J.: Arithmetic cycles on Picard modular surfaces and modular forms of Nebentypus. PreprintGoogle Scholar
  3. 3.
    Cogdell, J.: The Weil representation and cycles on Picard modular surfaces. PreprintGoogle Scholar
  4. 4.
    Harder, G.: On the cohomology of discrete arithmetically defined groups. In: Proc. Int. Colloq. on Discrete Subgroups of Lie Groups & Appl. to Moduli (Bombay 1973), 129–160. Oxford 1975Google Scholar
  5. 5.
    Hirzebruch, F., Zagier, D.: Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus. Invent. Math.36, 57–113 (1976)Google Scholar
  6. 6.
    Howe, R.: Remarks on classical invariant theory. PreprintGoogle Scholar
  7. 7.
    Kac, V.G.: Lie superalgebras. Adv. Math.26, 8–96 (1977)Google Scholar
  8. 8.
    Kashiwara, M., Vergne, M.: On the Segal-Shale-Weil representations and harmonic polynomials. Invent. Math.44, 1–47 (1978)CrossRefGoogle Scholar
  9. 9.
    Kudla, S.: Holomorphic Siegel modular forms associated to SO(n, 1). Math. Ann.256, 517–534 (1981)Google Scholar
  10. 10.
    Kudla, S.: On the integral of certain singular theta functions. J. Fac. Sci. Univ. Tokyo28, 439–463 (1981)Google Scholar
  11. 11.
    Kudla, S.: Periods of integrals for SU(n, 1). Compos. Math.50, 3–64 (1983)Google Scholar
  12. 12.
    Kudla, S.: Seesaw dual reductive pairs. In: Automorphic forms of several variables, Taniguchi Symposium, Katata, 1983; Prog. Math. Boston46 (1984)Google Scholar
  13. 13.
    Kudla, S., Millson, J.: The Poincaré dual of a geodesic algebraic curve in a quotient of the 2-ball. Can. J. Math.33, 485–499 (1979)Google Scholar
  14. 14.
    Kudla, S., Millson, J.: Harmonic differentials and closed geodesics on a Riemann surface. Invent. Math.54, 193–211 (1979)Google Scholar
  15. 15.
    Kudla, S., Millson, J.: Geodesic cycles and the Weil representation. I. Quotients of hyperbolic space and Siegel modular forms. Compos. Math.45, 207–271 (1982)Google Scholar
  16. 16.
    Kudla, S., Millson, J.: Tubes, cohomology with growth conditions and an application to the theta correspondence. PreprintGoogle Scholar
  17. 17.
    Kudla, S., Millson, J.: The theta correspondence and harmonic forms. II. PreprintGoogle Scholar
  18. 18.
    Millson, J.: Cycles and harmonic forms on locally symmetric spaces. Cand. Math. Bull.28, 3–38 (1985)Google Scholar
  19. 19.
    Oda, T.: On modular forms associated with indefinite quadratic forms of signature (2,n−2). Math. Ann.231, 97–144 (1977)Google Scholar
  20. 20.
    Schwermer, J.: Kohomologie arithmetisch definierter Gruppen und Eisensteinreihen. Lect. Notes Math. 988. Berlin, Heidelberg, New York: Springer 1983Google Scholar
  21. 21.
    Shintani, T.: On construction of holomorphic cusp forms of half integral weight. Nagaya Math. J.58, 83–126 (1975)Google Scholar
  22. 22.
    Tilgner, H.: Graded generalizations of Weyl and Clifford algebras. J. Pure Appl. Alg.10, 163–168 (1977)Google Scholar
  23. 23.
    Tong, Y.L., Wang, S.P.: Harmonic forms dual to geodesic cycles in quotients of SU(p, 1). Math. Ann.258, 298–318 (1982)Google Scholar
  24. 24.
    Tong, Y.L., Wang, S.P.: Theta functions defined by geodesic cycles in quotients of SU(p, 1). Invent. Math.71, 467–499 (1983)Google Scholar
  25. 25.
    Tong, Y.L., Wang, S.P.: Correspondence of Hermitian modular forms to cycles associated to SU(p, 2). J. Differ, Geom.18, 163–207 (1983)Google Scholar
  26. 26.
    Tong, Y.L., Wang, S.P.: Period integrals in non-compact quotients of SU(p, 1). Duke Math. J. (1985)Google Scholar
  27. 27.
    Wang, S.P.: Correspondence of modular forms to cycles associated toO(p, q). PreprintGoogle Scholar
  28. 28.
    Wang, S.P.: Correspondence of modular forms to cycles associated to Sp(p, q). PreprintGoogle Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Stephen S. Kudla
    • 1
  • John J. Millson
    • 2
  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA
  2. 2.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

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