On smoothing singularities of elliptic orbital integrals on GL(n) and Beyond Endoscopy

Recent work of Altuğ continues the preliminary analysis of Langlands' Beyond Endoscopy proposal for GL(2) by removing the contribution of the trivial representation by a Poisson summation formula. We show that Altuğ's method of smoothing real elliptic orbital integrals by an approximate functional equation extends to GL(n). We also discuss the case of an arbitrary reductive group, and remaining obstructions for applying Poisson summation.