On the absolute convergence of the spectral side of the Arthur trace   formula for GL(n)
  Let G be the group GL(n) over a number field E and let A be the ring of adeles of E. In this paper we prove that the spectral side of the Arthur trace formula for G is absolutely convergent for all integrable rapidly decreasing functions on $G(A)^1$. 
Werner Mueller, Birgit Speh, Erez M. Lapid