On the Siegel-Weil formula for classical groups over function fields

JOURNAL OF NUMBER THEORY

卷:215

Article

Xiong, Wei¹ 

[1] Hunan Univ, Sch Math, Changsha 410082, Hunan, Peoples R China

关键词: Siegel-Weil formula;    Classical groups;    Function fields;    Theta integral;    Siegel Eisenstein series;    Reduction theory;   

DOI  :  10.1016/j.jnt.2020.01.007

来源: Elsevier

【 摘 要 】

We establish a Siegel-Weil formula for classical groups over a function field with odd characteristic, which asserts in many cases that the Siegel Eisenstein series is equal to an integral of a theta function. This is a function-field analogue of the classical result proved by A. Weil in his 1965 Acta Math. paper. We also give a convergence criterion for the theta integral by using Harder's reduction theory over function fields. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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