Periods of integrals for S U ( n , 1 )

Stephen S. Kudla

Compositio Mathematica (1983)

  • Volume: 50, Issue: 1, page 3-63
  • ISSN: 0010-437X

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Kudla, Stephen S.. "Periods of integrals for $SU(n, 1)$." Compositio Mathematica 50.1 (1983): 3-63. <http://eudml.org/doc/89618>.

@article{Kudla1983,
author = {Kudla, Stephen S.},
journal = {Compositio Mathematica},
keywords = {dual reductive pairs; seesaw pair; rationality; periods of holomorphic forms; periods of binary theta series of weight two; special values of Eisenstein series of weight one},
language = {eng},
number = {1},
pages = {3-63},
publisher = {Martinus Nijhoff Publishers},
title = {Periods of integrals for $SU(n, 1)$},
url = {http://eudml.org/doc/89618},
volume = {50},
year = {1983},
}

TY - JOUR
AU - Kudla, Stephen S.
TI - Periods of integrals for $SU(n, 1)$
JO - Compositio Mathematica
PY - 1983
PB - Martinus Nijhoff Publishers
VL - 50
IS - 1
SP - 3
EP - 63
LA - eng
KW - dual reductive pairs; seesaw pair; rationality; periods of holomorphic forms; periods of binary theta series of weight two; special values of Eisenstein series of weight one
UR - http://eudml.org/doc/89618
ER -

References

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  2. [2] A.N. Andrianov and G.N. Maloletkin: Behavior of theta series of degree n under modular substitutions. Math. USSR Izvestija39 (1975) 227-241. Zbl0326.10025
  3. [3] A. Ash, D. Mumford, M. Rapapport and Y. Tai: Smooth Compactifications of locally symmetric varities. Math. Sci. Press. Brookline, Mass.1975. Zbl0334.14007MR457437
  4. [4] S. Gelbart: Examples of dual reductive pairs. Proc. Symp. Pure Math.33 part 1 (1979) 287-296. Zbl0425.22024MR546603
  5. [5] E. Hecke: Zur theorie der elliptischen modulfunktionen. Math. Annalen97 (1926) 210-242. Zbl52.0377.04JFM52.0377.04
  6. [6] E. Hecke: Bestimmung der perioden gewisser integrale durch die theorie der Klassenkörpern. Math. Zeit. 28 (1928) 708-727. Zbl54.0405.01MR1544986JFM54.0405.01
  7. [7] R. Howe and I.I. Piatetski-Shapiro: Some examples of automorphic forms on Sp 4. To appear. Zbl0529.22012MR700131
  8. [8] R. Howe: Invariant theory and duality for classical groups over finite fields. Preprint. 
  9. [9] R. Howe: θ-series and invariant theory. Proc. Symp. Pure Math.33 part 1 (1976) 275-285. Zbl0423.22016
  10. [10] S. Kudla and J. Millson: Geodesic cycles and the Weil representation I; Quotients of hyperbolic space and Siegel modular forms. Comp. Math.45 (1982) 207-271. Zbl0495.10016MR651982
  11. [11] S. Kudla: Holomorphic Siegel modular forms associated to SO(n, 1). Math. Annalen256 (1981) 517-534. Zbl0465.10020MR628232
  12. [12] S. Kudla: On the integrals of certain singular theta functions. J. Fac. Sci. Univ. Tokyo. Sec. IA, 28 (1982) 439-463. Zbl0511.10019MR656030
  13. [13] I. Satake: Holomorphic imbeddings of symmetric domains into a Siegel space. Amer. J. Math.87 (1965) 425-461. Zbl0144.08202MR196134
  14. [14] G. Shimura: On canonical models of arithmetic quotients of bounded symmetric domains. Ann. Math. 91 (1970) 144-222. Zbl0237.14009MR257031
  15. [15] G. Shimura: On the Fourier coefficients of modular forms of several variables. Göttingen, Nachr. Akad, Wiss. (1975) 261-268. Zbl0332.32024MR485706
  16. [16] G. Shimura: Theta functions with complex multiplication. Duke Math. J. 43 (1976) 673-696. Zbl0371.14022MR424705
  17. [17] G. Shimura: The arithmetic of automorphic forms with respect to a unitary group. Ann. Math. 107 (1978) 569-605. Zbl0409.10016MR563087
  18. [18] N. Wallach: L2-automorphic forms and cohomology classes on arithmetic quotients of SU(p, q). Preprint. Zbl0533.10025

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