Abstract
In this note, we prove a formula which expresses the constant term of the spherical Eisenstein series on a quasi-split unitary group as a linear combination of spherical Eisenstein series on smaller unitary groups.
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Gan W T, Ichino A. On endoscopy and the refined Gross-Prasad conjecture for (SO(5), SO(4)). J Inst Math Jussieu, 2011, 10: 235–324
Gan W T, Qiu Y, Takeda S. The regularized Siegel-Weil formula (the second term identity) and the Rallis inner product formula. Preprint, 2012
Gan W T, Takeda S. On the regularized Siegel-Weil formula (second term identity) and non-vanishing of theta lifts from orthogonal groups. J Reine Angew Math, 2011, 659: 175–244
Jiang D. Degree 16 standrad L-function of GSp(2) × GSp(2). Mem Amer Math Soc, 1996, 588
Jiang D. The first term identities for Eisenstein series. J Number Theory, 1998, 70: 67–98
Ichino A. A regularized Siegel-Weil formula for unitary groups. Math Z, 2004, 247: 241–277
Lai K F. Tamagawa numbers of reductive algebraic groups. Compos Math, 1980, 41: 153–188
Piatetski-Shapiro I, Rallis S. L-functions for the classical groups In: Lecture Notes in Mathematics vol. 1254, Berlin: Springer, 1987
Tan V. Poles of Siegel Eisenstein series on U(n, n). Canad J Math, 1999, 51: 164–175
Xiong W. A weak second term identity of the regularized Siegel-Weil formula for unitary groups. Math Z, in press, doi: 10.1007/s00209-012-1116-7
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Xiong, W. Constant terms of spherical Eisenstein series on quasi-split unitary groups. Sci. China Math. 56, 1751–1760 (2013). https://doi.org/10.1007/s11425-013-4686-x
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DOI: https://doi.org/10.1007/s11425-013-4686-x