arXiv subjects
Publications and source records attributed to Antonius Deitmar.
We give a detailed analysis of the orbit structure of the third power of the flag variety attached to SL(3,R). It turns out that 36 generalized Schubert cells split into 70 orbits plus one continuous family of orbits. On the latter, we construct invariant distributions and thus fill a gap in the literature by giving infinitely many linearly independent triple products of induced representations.
The theory of Ihara zeta functions is extended to infinite graphs which are weighted and of finite total weight. In this case one gets meromorphic instead of rational functions and the classical determinant formulas of Bass and Ihara hold true with Fredholm determinants.
The theory of Ihara zeta functions is extended to non-compact arithmetic quotients of Bruhat-Tits trees. This new zeta function turns out to be a rational function, despite the infinite-dimensional setting. In general it has zeros and poles, in contrast to the compact case. The determinant formulas of Bass and Ihara hold true if one defines the determinant as limit of all finite principal minors. From this analysis, a prime geodesic theorem is derived, which, applied to special arithmetic groups, yields new asymptotic assertions on class numbers of orders in global fields.