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arXiv · 1608.08475

A local relative trace formula for PGL(2)

Patrick Delorme·Pascale Harinck
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Abstract

Following a scheme inspired by B. Feigon, we describe the spectral side of a local relative trace formula for $G:= PGL(2,\rm E)$ relative to the symmetric subgroup $H:=PGL(2,\rm F)$ where $\rm E/\rm F$ is an unramified quadratic extension of local non archimedean fields of characteristic $0$. This spectral side is given in terms of regularized normalized periods and normalized $C$-functions of Harish-Chandra. Using the geometric side obtained in a more general setting by P. Delorme, P. Harinck and S. Souaifi , we deduce a local relative trace formula for $G$ relative to $H$. We apply our result to invert some orbital integrals.

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BibTeXRIS

Patrick Delorme, Pascale Harinck. 2016-08-30. A local relative trace formula for PGL(2). https://doi.org/10.2140/pjm.2017.291.121

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