We establish an infinitesimal variant of the Guo–Jacquet trace
formula for the case of a central simple algebra over a number field
containing a quadratic
field extension
.
It is an equality between a sum of geometric distributions on the tangent space of
some symmetric space and its Fourier transform. To prove this, we need to define
an analogue of Arthur’s truncation and then use the Poisson summation
formula. We describe the terms attached to regular semisimple orbits as explicit
weighted orbital integrals. To compare them to those for another case studied in
our previous work, we state and prove the weighted fundamental lemma
at the infinitesimal level by using Labesse’s work on the base change for
.
Keywords
Guo–Jacquet trace formula, Arthur's truncation, weighted
fundamental lemma
