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 $\mathrm{CM}_{D}$ (CM points of discriminant $D$) are equidistributed in $\mathcal F$. In this paper, 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 $\mathrm{CM}_D$ point lies on the boundary. Along the way, we also (conditionally) give a complete classification of negative discriminants with class group of small exponent.
| Comments: | 13 pages |
| Subjects: | Number Theory (math.NT) |
| MSC classes: | 11G15, 11R65, 11R29 |
| Cite as: | arXiv:2605.26020 [math.NT] |
| (or arXiv:2605.26020v1 [math.NT] for this version) | |
| https://doi.org/10.48550/arXiv.2605.26020 arXiv-issued DOI via DataCite (pending registration) |
From: Erick Ross [view email]
[v1]
Mon, 25 May 2026 16:40:51 UTC (13 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。