Geodesic
An infinitesimal variant of the Guo-Jacquet trace formula. I: The case of $(\mathrm{GL}_{2n, D}, \mathrm{GL}_{n, D}\times \mathrm{GL}_{n, D})$
Documenta mathematica, Tome 27 (2022), pp. 315-381 Cet article a éte moissonné depuis la source EMS Press

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We establish an infinitesimal variant of Guo-Jacquet trace formula for the case of (GL2n,D​,GLn,D​×GLn,D​). It is a kind of Poisson summation formula obtained by an analogue of Arthur's truncation process. It consists in the equality of the sums of two types of distributions which are non-equivariant in general: one type is associated to rational points in the categorical quotient, while the other type is the Fourier transform of the first type. For regular semi-simple points in the categorical quotient, we obtain weighted orbital integrals.
DOI : 10.4171/dm/872
Classification : 11F70, 11F72, 20G35
Mots-clés : Guo-Jacquet trace formula, Arthur's truncation 
@article{10_4171_dm_872,
     author = {Huajie Li},
     title = {An infinitesimal variant of the {Guo-Jacquet} trace formula. {I:} {The} case of $(\mathrm{GL}_{2n, D}, \mathrm{GL}_{n, D}\times \mathrm{GL}_{n, D})$},
     journal = {Documenta mathematica},
     pages = {315--381},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/872},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/872/}
}
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Huajie Li. An infinitesimal variant of the Guo-Jacquet trace formula. I: The case of $(\mathrm{GL}_{2n, D}, \mathrm{GL}_{n, D}\times \mathrm{GL}_{n, D})$. Documenta mathematica, Tome 27 (2022), pp. 315-381. doi: 10.4171/dm/872

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