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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.00995 |
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| _version_ | 1866912140362776576 |
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| author | Shankar, Arul Taniguchi, Takashi |
| author_facet | Shankar, Arul Taniguchi, Takashi |
| contents | We prove the existence of secondary terms of order $X^{3/4}$, with power saving error terms, in the counting functions of $|{\rm Sel}_2(E)|$, the 2-Selmer group of E, for elliptic curves E having height bounded by X. This is the first improvement on the error term of $o(X^{5/6})$, proved by Bhargava--Shankar, where the primary term of order $X^{5/6}$ for this counting function was obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00995 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Secondary terms in the first moment of $|{\rm Sel}_2(E)|$ Shankar, Arul Taniguchi, Takashi Number Theory We prove the existence of secondary terms of order $X^{3/4}$, with power saving error terms, in the counting functions of $|{\rm Sel}_2(E)|$, the 2-Selmer group of E, for elliptic curves E having height bounded by X. This is the first improvement on the error term of $o(X^{5/6})$, proved by Bhargava--Shankar, where the primary term of order $X^{5/6}$ for this counting function was obtained. |
| title | Secondary terms in the first moment of $|{\rm Sel}_2(E)|$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2412.00995 |