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

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S. Kudla, S. Rallis, On the Weil-Siegel formula, J. reine angew. , 387 (1988) 1-68. [KS] S. S. Kudla, W. J. Sweet, Degenerate principal series representations for U (n, n), Isr. J. , 98 (1997), 253-306. [LR] E. Lapid and S. Rallis, On the local factors of representations of classical groups, in J. , eds, Automorphic Representations, L-functions and Applications: Progress and Prospects, Berlin: de Gruyter, 309-359 (2005). [LZ] S. T. -B. Zhu, Degenerate principal series and local theta correspondence, Trans AMS, 350 (1998) 5017-5046.

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 . 7] are defined in terms of the K-rational basis of p+ H . 5] are defined in terms of the K rational ˆ and M ˆ H . Applying this structure of homogeneous vector bundles on M ˆ ×M ˆ in M ˆ H (cf. 7]) we see that the dual basis to the K-rational basis of pH chosen above can serve to define a canonical trivialization. 1 calculates the local zeta integral as an E-rational multiple of π pq , multiplied by the value f (1), where f is a discrete-series matrix coefficient.

Schriften, 209 (1990). [R] H. L. Resnikoff, Automorphic forms of singular weight are singular forms. Math. , 215 (1975), 173–193. [Ro] D. Rohrlich, On L-functions of elliptic curves and anticyclotomic towers. Invent. , 75 (1984) 383–408. [S1] G. Shimura, The special values of the zeta functions associated with cusp forms, Comm. Pure Appl. , 29 (1976), 783–804. [S2] G. Shimura, On Eisenstein series, Duke Math. , 50 (1983) 417-476. A SIMPLE PROOF OF RATIONALITY OF SIEGEL-WEIL EISENSTEIN SERIES 33 [S3] G.

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