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arXiv · 1908.00961

On the fine expansion of the unipotent contribution of the Guo-Jacquet trace formula

Pierre-Henri Chaudouard
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Abstract

For a useful class of functions (containing functions whose one finite component is essentially a matrix coefficient of a supercuspidal representation), we establish three results about the unipotent contribution of the Guo-Jacquet relative trace formula for the pair $(GL_n(D),GL_n(E))$. First we get a fine expansion in terms of global nilpotent integrals. Second we express these nilpotent integrals in terms of zeta integrals. Finally we prove that they satisfy certain homogeneity properties. The proof is based on a new kind of truncation introduced in a previous article.

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BibTeXRIS

Pierre-Henri Chaudouard. 2019-08-02. On the fine expansion of the unipotent contribution of the Guo-Jacquet trace formula. https://doi.org/10.2140/pjm.2020.305.539

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