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On the Siegel-Weil formula over function fields

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Wei,  Fu-Tsun
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Wei, F.-T. (2015). On the Siegel-Weil formula over function fields. Asian Journal of Mathematics, 19(3), 487-526. doi:10.4310/AJM.2015.v19.n3.a5.


Cite as: http://hdl.handle.net/21.11116/0000-0004-148C-8
Abstract
The aim of this article is to prove the Siegel-Weil formula over function fields for the dual reductive pair (Spn,O(V)), where Spn is the symplectic group of degree 2n and (V,QV) is an anisotropic quadratic space with even dimension. This is a function field analogue of Kudla and Rallis’ result. By this formula, the theta series is identified with the special value of the Siegel–Eisenstein series on Spn at a critical point.