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On the Siegel–Weil formula for unitary groups

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Abstract

Following S. S. Kudla and S. Rallis, we extend the Siegel–Weil formula for unitary groups, which relates a value of a Siegel Eisenstein series to the convergent integral of a theta function.

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References

  1. Guillemonat, A.: On some semispherical representations of an Hermitian symmetric pair of the tubular type. II. Construction of the unitary representations. Math. Ann. 246, 93–116 (1979/1980)

    Google Scholar 

  2. Harris, M.: A simple proof of rationality of Siegel–Weil Eisenstein series. preprint

  3. Harris, M., Li, J.-S., Skinner, C.M.: The Rallis inner product formula and p-adic L-functions. Automorphic representations, L-functions and applications: progress and prospects, pp. 225–255 Ohio State Univ. Math. Res. Inst. Publ. 11, de Gruyter (2005)

  4. Ichino A. (2001) On the regularized Siegel–Weil formula. J. Reine Angew. Math. 539, 201–234

    MathSciNet  MATH  Google Scholar 

  5. Ichino A. (2004) A regularized Siegel–Weil formula for unitary groups. Math. Z. 247, 241–277

    Article  MathSciNet  MATH  Google Scholar 

  6. Ikeda T. (1996) On the residue of the Eisenstein series and the Siegel–Weil formula. Compositio Math. 103, 183–218

    MathSciNet  MATH  Google Scholar 

  7. Kudla S.S. (1994) Splitting metaplectic covers of dual reductive pairs. Israel J. Math. 87, 361–401

    MathSciNet  MATH  Google Scholar 

  8. Kudla S.S., Rallis S. (1988) On the Weil–Siegel formula. J. Reine Angew. Math. 387, 1–68

    MathSciNet  MATH  Google Scholar 

  9. Kudla S.S., Rallis S. (1988) On the Weil–Siegel formula. II. The isotropic convergent case. J. Reine Angew. Math. 391, 65–84

    MathSciNet  MATH  Google Scholar 

  10. Kudla S.S., Rallis S. (1990) Degenerate principal series and invariant distributions. Israel J. Math. 69, 25–45

    MathSciNet  MATH  Google Scholar 

  11. Kudla S.S., Rallis S. (1994) A regularized Siegel–Weil formula: the first term identity. Ann. Math. 140, 1–80

    Article  MathSciNet  MATH  Google Scholar 

  12. Kudla S.S., Sweet W.J. Jr. (1997) Degenerate principal series representations for U(n,n) . Israel J. Math. 98, 253–306

    Article  MathSciNet  MATH  Google Scholar 

  13. Lee S.T. (1994) On some degenerate principal series representations of U(n,n) . J. Funct. Anal. 126, 305–366

    Article  MathSciNet  MATH  Google Scholar 

  14. Lee S.T., Zhu C.-B. (1998) Degenerate principal series and local theta correspondence. Trans. Am. Math. Soc. 350, 5017–5046

    Article  MathSciNet  Google Scholar 

  15. Mœglin,  C., Vignéras, M.-F., Waldspurger, J.-L.: Correspondances de Howe sur un corps p-adique. Lecture Notes in Mathematics, vol.1291. Springer, Berlin Heidelberg New York (1987)

  16. Murase, A., Sugano, T.: A note on Siegel–Weil formula for (U(2,1),U(2,2)). preprint

  17. Rallis S. (1984) On the Howe duality conjecture. Compositio Math. 51, 333–399

    MathSciNet  MATH  Google Scholar 

  18. Tan V. (1998) A regularized Siegel–Weil formula on U(2,2) and U(3) . Duke Math. J. 94, 341–378

    Article  MathSciNet  MATH  Google Scholar 

  19. Tan V. (1999) Poles of Siegel Eisenstein series on U(n,n) Can. J. Math. 51, 164–175

    MATH  Google Scholar 

  20. Weil A. (1965) Sur la formule de Siegel dans la théorie des groupes classiques. Acta Math. 113, 1–87

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Atsushi Ichino.

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Ichino, A. On the Siegel–Weil formula for unitary groups. Math. Z. 255, 721–729 (2007). https://doi.org/10.1007/s00209-006-0045-8

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  • DOI: https://doi.org/10.1007/s00209-006-0045-8

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