Geodesic cycles and the Weil representation I ; quotients of hyperbolic space and Siegel modular forms
Stephen S. Kudla; John J. Millson
Compositio Mathematica (1982)
- Volume: 45, Issue: 2, page 207-271
- ISSN: 0010-437X
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topKudla, Stephen S., and Millson, John J.. "Geodesic cycles and the Weil representation I ; quotients of hyperbolic space and Siegel modular forms." Compositio Mathematica 45.2 (1982): 207-271. <http://eudml.org/doc/89535>.
@article{Kudla1982,
author = {Kudla, Stephen S., Millson, John J.},
journal = {Compositio Mathematica},
keywords = {geodesic cycles; locally symmetric spaces; automorphic forms; harmonic forms; Poincare duals; discrete subgroups of SO(n,1); congruence subgroup; Weil representation; intersection numbers},
language = {eng},
number = {2},
pages = {207-271},
publisher = {Martinus Nijhoff Publishers},
title = {Geodesic cycles and the Weil representation I ; quotients of hyperbolic space and Siegel modular forms},
url = {http://eudml.org/doc/89535},
volume = {45},
year = {1982},
}
TY - JOUR
AU - Kudla, Stephen S.
AU - Millson, John J.
TI - Geodesic cycles and the Weil representation I ; quotients of hyperbolic space and Siegel modular forms
JO - Compositio Mathematica
PY - 1982
PB - Martinus Nijhoff Publishers
VL - 45
IS - 2
SP - 207
EP - 271
LA - eng
KW - geodesic cycles; locally symmetric spaces; automorphic forms; harmonic forms; Poincare duals; discrete subgroups of SO(n,1); congruence subgroup; Weil representation; intersection numbers
UR - http://eudml.org/doc/89535
ER -
References
top- [1] T. Asai: On the Doi-Naganuma lifting associated with imaginary quadratic fields, Nagoya Math. J., 71 (1978), 149-167. Zbl0357.10013MR509001
- [2] M. Berger, P. Gauduchon and E. Mazet, Le Spectre d'une Variété Riemannienne, Lecture Notes in Mathematics, 194, Springer-Verlag, New York. Zbl0223.53034
- [3] M. Gaffney: Asymptotic distributions associated with the Laplacian for forms, Comm. Pure and Appl. Math., XI (1958), 535-545. Zbl0102.09604MR99541
- [4] S. Gelbart: Examples of dual reductive pairs, Proc. Symp. Pure Math., 33 (1979), part 1, 287-296. Zbl0425.22024MR546603
- [5] W. Greub, S. Halperin and R. Vanstone: Connections, Curvature, and Cohomology, vol. I, Academic Press, New York and London, 1972. Zbl0322.58001MR336650
- [6] S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York and London, 1962. Zbl0111.18101MR145455
- [7] F. Hirzebruch and D. Zagier: Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus, Invent. Math., 36 (1976), 57-113. Zbl0332.14009MR453649
- [8] R. Howe: θ-series and invariant theory, Proc. Symp. Pure Math., 33 (1979), part 1, 275-285. Zbl0423.22016
- [9] G. Lion and M. Vergne: The Weil Representation, Maslov Index and Theta Series, Birkhäuser, Boston-Basel- Stuttgart, 1980. Zbl0444.22005MR573448
- [10] H. Klingen: Über Poincarésche Reihen vom Exponentialtyp, Math. Ann., 234 (1978), 145-157. Zbl0357.32019MR480357
- [11] M. Kneser: Strong approximation, Proc. Symp. Pure Math., vol. 9, A.M.S. (1966), 187-196. Zbl0201.37904MR213361
- [12] S. Kudla: Intersection numbers for quotients of the complex 2-ball and Hilbert modular forms, Invent. Math., 47 (1978), 189-208. Zbl0399.10030MR501929
- [13] S. Kudla and J. Millson: Harmonic differentials and closed geodesics on a Riemann surface, Invent. Math., 54 (1979), 193-211. Zbl0429.30038MR553218
- [14] H. Maass: Siegel's Modular Forms and Dirichlet Series, Lecture Notes in Mathematics, 216, Springer-Verlag, New York, 1971. Zbl0224.10028MR344198
- [15] J. Millson and M.S. Raghunathan: Geometric construction of cohomology of arithmetic groups I, to appear in the Patodi Memorial Issue of the Journal of the Indian Math. Soc. Zbl0524.22012MR592256
- [16] S. Niwa: Modular forms of half integral weight and the integral of certain theta function, Nagoya Math. J., 56 (1975), 147-163. Zbl0303.10027MR364106
- [17] O.T. O'Meara: Introduction to Quadratic Forms, Springer-Verlag, New York, 1971. Zbl0207.05304
- [18] T. Oda: On modular forms associated with indefinite quadratic forms of signature (2, n - 2), Math. Ann., 231 (1977), 97-144. Zbl0346.10013MR466026
- [19] W. Rossman: The structure of semisimple symmetric spaces, Journal of Canadian Math. Soc., 31 (1979), 157-180. Zbl0357.53033MR518716
- [20] A. Selberg: On the estimation of Fourier coefficients of modular forms, Proc. Symp. Pure Math., 10 (1965), 1-15. Zbl0142.33903MR182610
- [21] T. Shintani: On construction of holomorphic cusp forms of half integral weight, Nagoya Math. J., 58 (1975), 83-126. Zbl0316.10016MR389772
- [22] A. Weil: Sur certains groupes d'operateurs unitaires, Acta Math., 111 (1964), 143-211. Zbl0203.03305MR165033
- [23] D. Zagier: Modular forms associated to real quadratic fields, Invent. Math., 30 (1975), 1-46. Zbl0308.10014MR382174
- [24] D. Zagier: Modular forms whose Fourier coefficients involve zeta-functions of quadratic fields; Modular Functions of One Variable VI, Bonn; Lecture Notes in Math., 627, Springer-Verlag, New York, 1976. Zbl0372.10017MR485703
Citations in EuDML Documents
top- Niels O. Nygaard, Construction of some classes in the cohomology of Siegel modular threefolds
- Stephen S. Kudla, Periods of integrals for
- Stephen S. Kudla, John J. Millson, Intersection numbers of cycles on locally symmetric spaces and Fourier coefficients of holomorphic modular forms in several complex variables
- B. Brent Gordon, Intersections of higher weight cycles and modular forms
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