Zobrazeno 1 - 10
of 65
pro vyhledávání: '"11G05, 14H52"'
Autor:
Choi, Seokhyun, Im, Bo-Hae
We prove that if $f:X \rightarrow A$ is a morphism from a smooth projective variety $X$ to an abelian variety $A$ over a number field $K$, $G$ is a subgroup of automorphisms of $X$ satisfying certain properties, and if a prime $p$ divides the order o
Externí odkaz:
http://arxiv.org/abs/2410.16867
Autor:
Laishram, Shanta, Sahoo, Satyabrat
Let $K$ be a number field, and $\mathcal{O}_K$ be the ring of integers of $K$. In this article, we study the solutions of the generalized Fruit Diophantine equation $ax^d-y^2-z^2 +xyz-b=0$ over $K$, where $a\in \mathcal{O}_K\setminus \{0\}$, $b \in \
Externí odkaz:
http://arxiv.org/abs/2408.12278
Autor:
Stange, Katherine E.
Let $E$ be an elliptic curve with complex multiplication by a ring $R$, where $R$ is an order in an imaginary quadratic field or quaternion algebra. We define sesquilinear pairings ($R$-linear in one variable and $R$-conjugate linear in the other), t
Externí odkaz:
http://arxiv.org/abs/2405.14167
Autor:
Chiloyan, Garen
Let $N$ be a positive integer. Let $\operatorname{H}$ be a group of level $N$ and let $E$ be an elliptic curve defined over the rationals with $\textit{j}_{E} \neq 0, 1728$. Then the image $\overline{\rho}_{E,N}\left(\operatorname{Gal}\left(\overline
Externí odkaz:
http://arxiv.org/abs/2310.19987
Autor:
Roy, Subham
Following the work of Lal\'in and Mittal on the Mahler measure over arbitrary tori, we investigate the definition of the generalized Mahler measure for all Laurent polynomials in two variables when they do not vanish on the integration torus. We esta
Externí odkaz:
http://arxiv.org/abs/2308.04601
Autor:
Chiloyan, Garen
Let $\mathcal{E}$ be a $\mathbb{Q}$-isogeny class of elliptic curves defined over $\mathbb{Q}$ without CM. The isogeny graph associated to $\mathcal{E}$ is a graph which has a vertex for each elliptic curve in $\mathcal{E}$ and an edge for each $\mat
Externí odkaz:
http://arxiv.org/abs/2302.06094
Autor:
Chiloyan, Garen
Let $\mathcal{E}$ be a $\mathbb{Q}$-isogeny class of elliptic curves defined over $\mathbb{Q}$. The isogeny graph associated to $\mathcal{E}$ is a graph which has a vertex for each element of $\mathcal{E}$ and an edge for each $\mathbb{Q}$-isogeny of
Externí odkaz:
http://arxiv.org/abs/2208.11649
Autor:
Chiloyan, Garen
Let $\mathcal{E}$ be a $\mathbb{Q}$-isogeny class of elliptic curves defined over $\mathbb{Q}$. The isogeny graph associated to $\mathcal{E}$ is a graph which has a vertex for each element of $\mathcal{E}$ and an edge for each $\mathbb{Q}$-isogeny of
Externí odkaz:
http://arxiv.org/abs/2104.01128
Autor:
Salami, Sajad, Zargar, Arman Shamsi
We introduce a new generalization of $\theta$-congruent numbers by defining the notion of rational $\theta$-parallelogram envelope for a positive integer $n$, where $\theta \in (0, \pi)$ is an angle with rational cosine. Then, we study more closely s
Externí odkaz:
http://arxiv.org/abs/2012.13471
Autor:
Salami, Sajad, Zargar, Arman Shamsi
A positive integer $N$ is called a $\theta$-congruent number if there is a $\ta$-triangle $(a,b,c)$ with rational sides for which the angle between $a$ and $b$ is equal to $\theta$ and its area is $N \sqrt{r^2-s^2}$, where $\theta \in (0, \pi)$, $\co
Externí odkaz:
http://arxiv.org/abs/2012.13451