La variante infinitésimale de la formule des traces de Jacquet-Rallis pour les groupes unitaires

الأصل · EN

We establish an infinitesimal version of the Jacquet-Rallis trace formula for unitary groups. Our formula is obtained by integrating a truncated kernel à la Arthur. It has a geometric side which is a sum of distributions Jₒ indexed by classes of elements of the Lie algebra of U(n+1) stable by U(n)-conjugation as well as the "spectral side" consisting of the Fourier transforms of the aforementioned distributions. We prove that the distributions Jₒ are invariant and depend only on the choice of the Haar measure on U(n)(A). For regular semi-simple classes o, Jₒ is a relative orbital integral of Jacquet-Rallis. For classes o called relatively regular semi-simple, we express Jₒ in terms of relative orbital integrals regularised by means of zêta functions.