Central $L$ values of congruent number elliptic curves
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909621859385344 |
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| author | Guo, Xuejun Ye, Dongxi Yin, Hongbo |
| author_facet | Guo, Xuejun Ye, Dongxi Yin, Hongbo |
| contents | Let $E_n$ be the congruent number elliptic curve $y^2=x^3-n^2x$, where $n$ is square-free and not divisible by primes $p\equiv 3\pmod 4$. In this paper, we prove that $L(E_n,1)$ can be expressed as the square of CM values of some simple theta functions, generalizing two classical formulas of Gauss. Our result is meaningful in both theory and practical computation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13133 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Central $L$ values of congruent number elliptic curves Guo, Xuejun Ye, Dongxi Yin, Hongbo Number Theory Let $E_n$ be the congruent number elliptic curve $y^2=x^3-n^2x$, where $n$ is square-free and not divisible by primes $p\equiv 3\pmod 4$. In this paper, we prove that $L(E_n,1)$ can be expressed as the square of CM values of some simple theta functions, generalizing two classical formulas of Gauss. Our result is meaningful in both theory and practical computation. |
| title | Central $L$ values of congruent number elliptic curves |
| topic | Number Theory |
| url | https://arxiv.org/abs/2505.13133 |