2015/10/14 by Michał Zydor, Zydor, Michał
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT
paper · pdf · doi:10.48550/arxiv.1510.04301
in French
arxiv created 2015/10/14 · arxiv updated 2015/10/16
We establish the coarse relative trace formulae of Jacquet-Rallis for linear and unitary groups. Both formulae are of the form: a sum of spectral distributions equals a sum of geometric distributions. In order to obtain the spectral decompositions we introduce new truncation operators and we investigate their properties. On the geometric side, by means of the Cayley transform, the decompositions are derived from a procedure of descent to the tangent spaces for which the formulae are known thanks to our previous work.