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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.28614 |
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| _version_ | 1866914608618405888 |
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| author | Ross, Erick Xue, Hui |
| author_facet | Ross, Erick Xue, Hui |
| contents | In 1988, William Duke showed that CM points of fundamental discriminant $D$ are equidistributed in the complex upper half-plane $\mathcal H$ as $D \to -\infty$. He also showed a similar result for RM curves (a positive discriminant analog of CM points). In this paper, we investigate analogous problems concerning the distribution of CM points and RM curves along fixed geodesics in $\mathcal H$, and around fixed points in $\mathcal H$. Specifically, we show that CM points and RM curves are equidistributed along every fixed rational geodesic in $\mathcal H$, and around every fixed CM point in $\mathcal H$. To prove these results, we solve the aggregate Linnik problem for arbitrary binary quadratic forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28614 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equidistribution of CM points and RM curves Ross, Erick Xue, Hui Number Theory 11G15, 11E16 In 1988, William Duke showed that CM points of fundamental discriminant $D$ are equidistributed in the complex upper half-plane $\mathcal H$ as $D \to -\infty$. He also showed a similar result for RM curves (a positive discriminant analog of CM points). In this paper, we investigate analogous problems concerning the distribution of CM points and RM curves along fixed geodesics in $\mathcal H$, and around fixed points in $\mathcal H$. Specifically, we show that CM points and RM curves are equidistributed along every fixed rational geodesic in $\mathcal H$, and around every fixed CM point in $\mathcal H$. To prove these results, we solve the aggregate Linnik problem for arbitrary binary quadratic forms. |
| title | Equidistribution of CM points and RM curves |
| topic | Number Theory 11G15, 11E16 |
| url | https://arxiv.org/abs/2605.28614 |