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Extra resources for A Simple Proof of Rationality of Siegel-Weil Eisenstein Series(en)(33s)

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Harris, S. Kudla, W. J. Sweet, Theta dichotomy for unitary groups, JAMS, 9 (1996) 941-1004. [HKS] M. Harris, S. Zucker, Boundary Cohomology of Shimura Varieties, III, M´emoires Soc. Math. France, 85 (2001). [Ho] R. , 880 (1980) 211-248. [I1] A. Ichino, A regularized Siegel-Weil formula for unitary groups, Math. , 247 (2004) 241-277. [I2] A. Ichino, On the Siegel-Weil formula for unitary groups, manuscript, (2005). [K] S. S. Kudla, Splitting metaplectic covers of dual reductive pairs, Israel J.

American Mathematical Society (2000). [T] V. Tan, Poles of Siegel Eisenstein series on U (n, n), Can. J. , 51 (1999), 164-175. [W] A. , 113 (1965) 1-87.

3). The main point of the comparison is that Jµ,κ is a rational function on the algebraic group H, defined over K. 4 ˆ and M ˆ H and the corresponding HarishSince the rational structures on M Chandra decompositions are compatible, we are now in the situation considered by Garrett. 11]. It remains to show that the rational structure considered above is also the one used to define archimedean zeta integrals in [H3]. e. in terms of functions in the induced representation, cf. 3]. By the results of [H1,§5], the archimedean condition for rationality of the constant term is compatible up to K with rationality of Jµ,κ .

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