Upper bounds for analytic ranks of elliptic curves over cyclotomic fields
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916632982454272 |
|---|---|
| author | Dasgupta, Agniva Khan, Rizwanur |
| author_facet | Dasgupta, Agniva Khan, Rizwanur |
| contents | Let $E$ be an elliptic curve defined over $\mathbb{Q}$. We show that the analytic rank of $E$ over the cyclotomic extension $\mathbb{Q}(e^{2πi/q})$ is bounded above by $q^{45/52+\varepsilon}$, as $q\to \infty$ through the primes. This improves the bound $q^{7/8+\varepsilon}$ established by Chinta. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19566 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Upper bounds for analytic ranks of elliptic curves over cyclotomic fields Dasgupta, Agniva Khan, Rizwanur Number Theory Let $E$ be an elliptic curve defined over $\mathbb{Q}$. We show that the analytic rank of $E$ over the cyclotomic extension $\mathbb{Q}(e^{2πi/q})$ is bounded above by $q^{45/52+\varepsilon}$, as $q\to \infty$ through the primes. This improves the bound $q^{7/8+\varepsilon}$ established by Chinta. |
| title | Upper bounds for analytic ranks of elliptic curves over cyclotomic fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2502.19566 |