On the functional equation of the Siegel series

Tamotsu Ikeda

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arXiv · 1506.01178

On the functional equation of the Siegel series

Tamotsu Ikeda

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Abstract

It is well-known that the Fourier coefficients of Siegel-Eisenstein series can be expressed in terms of the Siegel series. The functional equation of the Siegel series of a quadratic form over $\mathbb{Q}_p$ was first proved by Katsurada. In this paper, we prove the functional equation of the Siegel series over a non-archimedean local field by using the representation theoretic argument by Kudla and Sweet.

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Tamotsu Ikeda. 2015-06-03. On the functional equation of the Siegel series. https://arxiv.org/abs/1506.01178

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