Erick.RossAffiliation: Clemson University Title Of Talk: Boundary CM points and Class Groups of Small Exponent
URLS: Abstract: Let $\mathcal F$ denote the fundamental domain for $\text{SL}_2(\mathbb{Z})$ on the upper half plane $\mathcal H$. William Duke showed that as fundamental discriminants $D \to -\infty$, the sets $\textnormal{CM}_{D}$ (CM points of discriminant $D$) are equidistributed in $\mathcal F$. In this talk, we investigate the behavior of CM points on the boundary of $\mathcal F$. We prove that such CM points are equidistributed on the boundary, and also give a complete characterization of when every $\textnormal{CM}_D$ point lies on the boundary. Along the way, we also (conditionally) give a complete classification of negative discriminants with class group of small exponent.
WARNING: This page contains MATH-JAX
Last update made Tue Mar 10 21:28:05 CDT 2026.
|