Zobrazeno 1 - 10
of 101
pro vyhledávání: '"11G05, 11G07"'
In this paper, we consider a version of the bias conjecture for second moments in the setting of elliptic curves over finite fields whose trace of Frobenius lies in an arbitrary fixed arithmetic progression. Contrary to the classical setting of reduc
Externí odkaz:
http://arxiv.org/abs/2405.14234
Let $E_{1}$ and $E_{2}$ be elliptic curves defined over a number field $K$. We say that $E_{1}$ and $E_{2}$ are discriminant ideal twins if they are not $K$-isomorphic and have the same minimal discriminant ideal and conductor. Such curves are said t
Externí odkaz:
http://arxiv.org/abs/2402.19183
Autor:
Vavasour, Thomas, Wuthrich, Christian
We study the action of the Galois group $G$ of a finite extension $K/k$ of number fields on the points on an elliptic curve $E$. For an odd prime $p$, we aim to determine the structure of the $p$-adic completion of the Mordell-Weil group $E(K)$ as a
Externí odkaz:
http://arxiv.org/abs/2306.13365
A generalization of the congruent number problem is to find positive integers $n$ that appear as the areas of Heron triangles. Selmer group of a congruent number elliptic curve has been studied quite extensively. Here, we look into the $2$-Selmer gro
Externí odkaz:
http://arxiv.org/abs/2301.08099
Rank computation of an elliptic curve is one of the most important problems in number theory due to its importance in various open questions in number theory. A common way to understand this rank is via understanding the Selmer group and the Shafarev
Externí odkaz:
http://arxiv.org/abs/2301.03486
Autor:
Tan, Ki-Seng
For an elliptic curve A defined over a global function field K of characteristic p>0, the p-Selmer group of the Frobenius twist of A tends to have larger order than that of A. The aim of this note is to discuss this phenomenon.
Comment: 25 pages
Comment: 25 pages
Externí odkaz:
http://arxiv.org/abs/2301.00518
Given an integer n>1, it is a classical Diophantine problem that whether n can be written as a sum of two rational cubes. The study of this problem, considering several special cases of n, has a copious history that can be traced back to the works of
Externí odkaz:
http://arxiv.org/abs/2211.17118
Given any positive integer n, it is well known that there always exist triangles with rational sides a, b and c such that the area of the triangle is n. Assuming finiteness of the Shafarevich-Tate group, we first construct a family of infinitely many
Externí odkaz:
http://arxiv.org/abs/2206.02475
Autor:
Naskręcki, Bartosz, Verzobio, Matteo
Publikováno v:
Proceedings of the Royal Society of Edinburgh Section A: Mathematics (2024)
In this note we prove a formula for the cancellation exponent $k_{v,n}$ between division polynomials $\psi_n$ and $\phi_n$ associated with a sequence $\{nP\}_{n\in\mathbb{N}}$ of points on an elliptic curve $E$ defined over a discrete valuation field
Externí odkaz:
http://arxiv.org/abs/2203.02015
Autor:
Melistas, Mentzelos
Let $K$ be a global field and let $E/K$ be an elliptic curve with a $K$-rational point of prime order $p$. In this paper we are interested in how often the (global) Tamagawa number $c(E/K)$ of $E/K$ is divisible by $p$. This is a natural question to
Externí odkaz:
http://arxiv.org/abs/2202.06235