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Recent work of Altu\u{g} continues the preliminary analysis of Langlands'Beyond Endoscopy proposal for $GL(2)$ by removing the contribution of thetrivial representation to the trace formula using a Poisson summation formula.We show that Altu\u{g}'s method of smoothing real elliptic orbital integrals byan approximate functional equation extends to $GL(n)$. We also discuss the caseof an arbitrary reductive group, and remaining obstructions for applyingPoisson summation.

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