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

How to cite

top

Kudla, 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. [1] T. Asai: On the Doi-Naganuma lifting associated with imaginary quadratic fields, Nagoya Math. J., 71 (1978), 149-167. Zbl0357.10013MR509001
  2. [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. [3] M. Gaffney: Asymptotic distributions associated with the Laplacian for forms, Comm. Pure and Appl. Math., XI (1958), 535-545. Zbl0102.09604MR99541
  4. [4] S. Gelbart: Examples of dual reductive pairs, Proc. Symp. Pure Math., 33 (1979), part 1, 287-296. Zbl0425.22024MR546603
  5. [5] W. Greub, S. Halperin and R. Vanstone: Connections, Curvature, and Cohomology, vol. I, Academic Press, New York and London, 1972. Zbl0322.58001MR336650
  6. [6] S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York and London, 1962. Zbl0111.18101MR145455
  7. [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. [8] R. Howe: θ-series and invariant theory, Proc. Symp. Pure Math., 33 (1979), part 1, 275-285. Zbl0423.22016
  9. [9] G. Lion and M. Vergne: The Weil Representation, Maslov Index and Theta Series, Birkhäuser, Boston-Basel- Stuttgart, 1980. Zbl0444.22005MR573448
  10. [10] H. Klingen: Über Poincarésche Reihen vom Exponentialtyp, Math. Ann., 234 (1978), 145-157. Zbl0357.32019MR480357
  11. [11] M. Kneser: Strong approximation, Proc. Symp. Pure Math., vol. 9, A.M.S. (1966), 187-196. Zbl0201.37904MR213361
  12. [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. [13] S. Kudla and J. Millson: Harmonic differentials and closed geodesics on a Riemann surface, Invent. Math., 54 (1979), 193-211. Zbl0429.30038MR553218
  14. [14] H. Maass: Siegel's Modular Forms and Dirichlet Series, Lecture Notes in Mathematics, 216, Springer-Verlag, New York, 1971. Zbl0224.10028MR344198
  15. [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. [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. [17] O.T. O'Meara: Introduction to Quadratic Forms, Springer-Verlag, New York, 1971. Zbl0207.05304
  18. [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. [19] W. Rossman: The structure of semisimple symmetric spaces, Journal of Canadian Math. Soc., 31 (1979), 157-180. Zbl0357.53033MR518716
  20. [20] A. Selberg: On the estimation of Fourier coefficients of modular forms, Proc. Symp. Pure Math., 10 (1965), 1-15. Zbl0142.33903MR182610
  21. [21] T. Shintani: On construction of holomorphic cusp forms of half integral weight, Nagoya Math. J., 58 (1975), 83-126. Zbl0316.10016MR389772
  22. [22] A. Weil: Sur certains groupes d'operateurs unitaires, Acta Math., 111 (1964), 143-211. Zbl0203.03305MR165033
  23. [23] D. Zagier: Modular forms associated to real quadratic fields, Invent. Math., 30 (1975), 1-46. Zbl0308.10014MR382174
  24. [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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.