The trace class conjecture and the Weyl upper bound on the discrete spectrum of arithmetic groups (Q1372888)

The note announces a solution of the trace class conjecture and a Weyl law upper bound on the discrete spectrum of an arithmetic subgroup of a semisimple algebraic group over the rationals. Use is made of a preprint by the author as well as the author's paper ``The Weyl upper bound on the discrete spectrum of locally symmetric spaces,'' to appear in J. Differ. Geom. Another reference is \textit{W. Mueller} [Ann. Math., II. Ser. 130, 473-529 (1989; Zbl 0701.11019)]. In the special case of \(GL(n,\mathbb Z)\) some other references on Weyl's law are \textit{E. Stade} and \textit{D. I. Wallace} [Pac. J. Math. 173, 241-261 (1996; Zbl 0849.11045)] and \textit{J. Huntley} [Trans. Am. Math. Soc. 332, 875-888 (1992; Zbl 0753.11022)].