Groups, Geometry, and Dynamics


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Volume 5, Issue 2, 2011, pp. 367–391
DOI: 10.4171/GGD/132

On the Arthur–Selberg trace formula for GL(2)

Tobias Finis (1) and Erez Lapid (2)

(1) Mathematisches Institut, Heinrich-Heine-Universität, Universitätsstraße 1, 40225, DÜSSELDORF, GERMANY
(2) Einstein Institute of Mathematics, Hebrew University, Givat Ram, 91904, JERUSALEM, ISRAEL

We extend the terms on the geometric side of the trace formula for GL(2) over $\mathbb{Q}$ continuously to a natural Fréchet algebra of non-compactly supported test functions. For the spectral side the analogous result had been obtained previously (in much greater generality) in collaboration with W. Müller.

Keywords: Trace formula, automorphic forms