The hyperbolic circle problem over Heegner points
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916796244688896 |
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| author | Chatzakos, Dimitrios Cherubini, Giacomo Lester, Stephen Risager, Morten S. |
| author_facet | Chatzakos, Dimitrios Cherubini, Giacomo Lester, Stephen Risager, Morten S. |
| contents | For the full modular group, we obtain a logarithmic improvement on Selberg's long-standing bound for the error term of the counting function in the hyperbolic circle problem over Heegner points of different discriminants. The main ingredients in our method are Waldspurger's formula, twisted first moments of certain Rankin-Selberg convolutions, and a new fractional moment estimate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13883 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The hyperbolic circle problem over Heegner points Chatzakos, Dimitrios Cherubini, Giacomo Lester, Stephen Risager, Morten S. Number Theory 11P21 11N45 11F67, For the full modular group, we obtain a logarithmic improvement on Selberg's long-standing bound for the error term of the counting function in the hyperbolic circle problem over Heegner points of different discriminants. The main ingredients in our method are Waldspurger's formula, twisted first moments of certain Rankin-Selberg convolutions, and a new fractional moment estimate. |
| title | The hyperbolic circle problem over Heegner points |
| topic | Number Theory 11P21 11N45 11F67, |
| url | https://arxiv.org/abs/2506.13883 |