Zobrazeno 1 - 10
of 27
pro vyhledávání: '"11G05, 11R45"'
Autor:
Hatley, Jeffrey, Ray, Anwesh
We study the distribution of ranks of elliptic curves in quadratic twist families using Iwasawa-theoretic methods, contributing to the understanding of Goldfeld's conjecture. Given an elliptic curve $ E/\mathbb{Q} $ with good ordinary reduction at $
Externí odkaz:
http://arxiv.org/abs/2412.07308
Autor:
Müller, Katharina, Ray, Anwesh
Let $E_{/\mathbb{Q}}$ be an elliptic curve and $p$ an odd prime such that $E$ has good ordinary reduction at $p$ and the Galois representation on $E[p]$ is irreducible. Then Greenberg's $\mu=0$ conjecture predicts that the Selmer group of $E$ over th
Externí odkaz:
http://arxiv.org/abs/2409.15056
Autor:
Ray, Anwesh, Shingavekar, Pratiksha
Let $p \in \{3, 5\}$ and consider a cyclic $p$-extension $L/\mathbb{Q}$. We show that there exists an effective positive density of elliptic curves $ E $ defined over $ \mathbb{Q} $, ordered by height, that are diophantine stable in $ L $.
Comme
Comme
Externí odkaz:
http://arxiv.org/abs/2406.12561
Autor:
Ray, Anwesh, Shingavekar, Pratiksha
Let $a$ be an integer which is not of the form $n^2$ or $-3 n^2$ for $n\in \mathbb{Z}$. Let $E_a$ be the elliptic curve with rational $3$-isogeny defined by $E_a:y^2=x^3+a$, and $K:=\mathbb{Q}(\mu_3)$. Assume that the $3$-Selmer group of $E_a$ over $
Externí odkaz:
http://arxiv.org/abs/2403.18034
In this paper, we prove that when elliptic curves over $\mathbb{Q}$ are ordered by height, the second moment of the size of the $2$-Selmer group is at most $15$. This confirms a conjecture of Poonen and Rains.
Comment: 49 pages
Comment: 49 pages
Externí odkaz:
http://arxiv.org/abs/2110.09063
For an elliptic curve $E$ defined over a number field $K$, the heuristic density of the set of primes of $K$ for which $E$ has cyclic reduction is given by an inclusion-exclusion sum $\delta_{E/K}$ involving the degrees of the $m$-division fields $K_
Externí odkaz:
http://arxiv.org/abs/2001.00028
Autor:
Kane, Daniel, Klagsbrun, Zev
If $E$ is an elliptic curve with a point of order two, then work of Klagsbrun and Lemke Oliver shows that the distribution of $\dim_{\mathbb{F}_2}\mathrm{Sel}_\phi(E^d/\mathbb{Q}) - \dim_{\mathbb{F}_2} \mathrm{Sel}_{\hat\phi}(E^{\prime d}/\mathbb{Q})
Externí odkaz:
http://arxiv.org/abs/1702.02687
Autor:
Smith, Alexander
We prove that the $2^\infty$-class groups of the imaginary quadratic fields have the distribution predicted by the Cohen-Lenstra heuristic. Given an elliptic curve E/Q with full rational 2-torsion and no rational cyclic subgroup of order four, we ana
Externí odkaz:
http://arxiv.org/abs/1702.02325
The elliptic curve $E_k \colon y^2 = x^3 + k$ admits a natural 3-isogeny $\phi_k \colon E_k \to E_{-27k}$. We compute the average size of the $\phi_k$-Selmer group as $k$ varies over the integers. Unlike previous results of Bhargava and Shankar on $n
Externí odkaz:
http://arxiv.org/abs/1610.05759
Autor:
Bhargava, Manjul, Skinner, Christopher
We prove that, when all elliptic curves over $\mathbb{Q}$ are ordered by naive height, a positive proportion have both algebraic and analytic rank one. It follows that the average rank and the average analytic rank of elliptic curves are both strictl
Externí odkaz:
http://arxiv.org/abs/1401.0233