The spectrum of an Adelic Markov operator Andreas Knauf 11K7037A3037D35ergodicityprobabilistic number theoryrepresentation theory For unitary representations of $\mathrm{SL}(2,\mathbb{Z})$, and with $\mathbf{L}$ and $\mathbf{R}$ representing $\left(\begin{smallmatrix}1&1\\0&1\end{smallmatrix}\right)$ (respectively, $\left(\begin{smallmatrix}1&0\\1&1\end{smallmatrix}\right)$), we analyze the operators $\mathbf{T}:=\frac{1}{2}(\mathbf{L}+\mathbf{R})$. Indiana University Mathematics Journal 2015 text pdf 10.1512/iumj.2015.64.5655 10.1512/iumj.2015.64.5655 en Indiana Univ. Math. J. 64 (2015) 1465 - 1512 state-of-the-art mathematics http://iumj.org/access/