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Theta functions defined by geodesic cycles in quotients ofSU(p, 1)

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References

  1. Becker, H.: Poincarésche Reihen zur hermitischen Modulgruppe. Math. Annalen129, 187–208 (1955)

    Google Scholar 

  2. Braun, H.: Darstellung hermitischer Modulformen durch Poincarésche Reihen. Abh. Math. Sem. Univ. Hamburg22, 9–37 (1958)

    Google Scholar 

  3. 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 

  4. Igusa, J.: Theta functions. Berlin-Heidelberg-New York: Springer 1972

    Google Scholar 

  5. Klingen, H.: Über Poincarésche Reihen vom Exponentialtyp. Math. Ann.234, 145–157 (1978)

    Google Scholar 

  6. Kudla, S.: Intersection numbers for quotients of the complex 2-ball and Hilbert modular forms. Invent. Math.47, 189–208 (1978)

    Google Scholar 

  7. Kudla, S.: On certain arithmetic automorphic forms forSU(1,q). Invent. Math.52, 1–25 (1979)

    Google Scholar 

  8. Kudla, S., Millson, J.: Geodesic cycles and the Weil representation I: Quotients of the hyperbolic space and Siegel modular forms. Comp. Math.45, 207–271 (1982)

    Google Scholar 

  9. Niwa, S.: Modular forms of half integral weight and the integral of certain theta functions. Nagoya Math. J.56, 147–163 (1975)

    Google Scholar 

  10. Oda, T.: On modular forms associated with indefinite quadratic forms of signature (2,n−2). Math. Annalen231, 97–144 (1977)

    Google Scholar 

  11. Ragunathan, M.S.: Cohomology of arithmetic subgroups of algebraic groups I. Ann. of Math.86, 409–424 (1967)

    Google Scholar 

  12. Shintani, T.: On construction of holomorphic cusp forms of half integral weight. Nagoya Math.58, 83–126 (1975)

    Google Scholar 

  13. Tong, Y.L., Wang, S.P.: Harmonic forms dual to geodesic cycles in quotients ofSU(p,1). Math. Ann.258, 289–318 (1982)

    Google Scholar 

  14. Zagier, D.: Modular forms whose Fourier coefficients involve zeta-functions of quadratic fields. Modular functions of one variable VI, Bonn. Lecture Notes in Math. vol. 627. Berlin-Heidelberg-New York: Springer 1976

    Google Scholar 

  15. Weil, A.: Varietes Kahleriennes. Paris: Hermann 1971

    Google Scholar 

  16. Wells, R.O.: Differential Analysis on complex manifolds. Englewood Cliffs, N.J.: Prentice Hall 1973

    Google Scholar 

  17. Oda, T.: Periods of Hilbert modular surfaces. Progress in Mathematics, vol. 19. Birkhäuser 1982

  18. Hirzebruch, F., Geer, van der, G.: Lectures on Hilbert modular surfaces. Sem. Math. Sup., Les Presses de L'Université de Montreal 1981

  19. Siegel, C.L.: On the theory of indefinite quadratic forms. Annals of Math.45, 577–622 (1944)

    Google Scholar 

  20. Siegel, C.L.: Über die Fourierschen Koeffizienten der Eisensteinschen Reihen. Mat.-Fys. Med. Kong. Danske Vid. Selskab34, (No. 6) (1964)

  21. Shintani, T.: On automorphic forms on unitary groups of order 3. (preprint)

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  1. Department of Mathematics, Purdue University, 47907, West Lafayette, IN, USA

    Y. L. Tong & S. P. Wang

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  1. Y. L. Tong
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  2. S. P. Wang
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First named author supported in part by NSF through grants MCS 79-03798 and MCS 77-18723 AO4. Second named author supported in part by MCS 79-00695

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Tong, Y.L., Wang, S.P. Theta functions defined by geodesic cycles in quotients ofSU(p, 1). Invent Math 71, 467–499 (1983). https://doi.org/10.1007/BF02095988

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