Asymptotic formulas are established for identity, unipotent, and hyperbolic contributions to the GL2 trace formula over Q with ramification, using contour shifts and hyperbolic Poisson summation to connect geometric and spectral sides.
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Beyond endoscopy for $\mathsf{GL}_2$ over $\mathbb{Q}$ with ramification 4: contribution of non-elliptic parts
Asymptotic formulas are established for identity, unipotent, and hyperbolic contributions to the GL2 trace formula over Q with ramification, using contour shifts and hyperbolic Poisson summation to connect geometric and spectral sides.