Stabilization of periods of Eisenstein series and Bessel distributions on \(GL(3)\) relative to \(U(3)\)
Let \(E/F\) be a quadratic extension of number fields, let \(G = \text{Res}_{E/F} \text{GL}(3)\) and let \(H\) be the quasi-split \(\text{U}(3)\) relative to \(E/F\). In the relative trace formula for the pair \((G,H)\), distributions involving (regularized) periods of automorphic forms on \(G\) appear at the spectral side. These ``relative Bessel distributions'' are matched with ``Bessel distributions'' on \(G' = \text{GL}(3)\) in case they correspond to cuspidal representations. In the present paper, a stabilization of the relative Bessel distributions corresponding to Eisenstein series is defined, and it is proved that the stabilized distributions match with Bessel distributions on \(G'\). The stabilization is effectuated writing the regularized period of an Eisenstein series as a sum of four factorizable distributions. The local factors at the unramified places are expressed in terms of \(L\)-functions, a computation for which the authors used Mathematica.
scientific article; zbMATH DE number 1477085