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pro vyhledávání: '"A, Szymaszkiewicz"'
Let $K = \mathbb Q(\sqrt{-q})$, where $q$ is a prime congruent to $3$ modulo $4$. Let $A = A(q)$ denote the Gross curve over the Hilbert class field $H$ of $K$. In this note we use Magma to calculate the values $L(E/H, 1)$ for all such $q$'s up to so
Externí odkaz:
http://arxiv.org/abs/2109.03802
We exhibit $88$ examples of rank zero elliptic curves over the rationals with $|\sza(E)| > 63408^2$, which was the largest previously known value for any explicit curve. Our record is an elliptic curve $E$ with $|\sza(E)| = 1029212^2 = 2^4\cdot 79^2
Externí odkaz:
http://arxiv.org/abs/2103.11001
Let $K=\Bbb Q(\sqrt{-q})$, where $q$ is a prime congruent to $3$ modulo $4$. Let $A=A(q)$ denote the Gross curve. Let $E=A^{(-\beta)}$ denote its quadratic twist, with $\beta=\sqrt{-q}$. The curve $E$ is defined over the Hilbert class field $H$ of $K
Externí odkaz:
http://arxiv.org/abs/1904.08691
Akademický článek
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This paper continues the authors previous investigations concerning orders of Tate-Shafarevich groups in quadratic twists of a given elliptic curve, and for the family of the Neumann-Setzer type elliptic curves. Here we present the results of our sea
Externí odkaz:
http://arxiv.org/abs/1803.06932
We present the results of our search for the orders of Tate-Shafarevich groups for the Neumann-Setzer type elliptic curves.
Comment: submitted. arXiv admin note: text overlap with arXiv:1611.07840
Comment: submitted. arXiv admin note: text overlap with arXiv:1611.07840
Externí odkaz:
http://arxiv.org/abs/1611.08181
We present the results of our search for the orders of Tate-Shafarevich groups for the quadratic twists of elliptic curves. We formulate a general conjecture, giving for a fixed elliptic curve $E$ over $\Bbb Q$ and positive integer $k$, an asymptotic
Externí odkaz:
http://arxiv.org/abs/1611.07840
Autor:
Stȩpień, Zofia, Misiak, Aleksander, Szymaszkiewicz, Alicja, Szymaszkiewicz, Lucjan, Zwierzchowski, Maciej
In this paper we show that at most $2 \gcd(m,n)$ points can be placed with no three in a line on an $m\times n$ discrete torus. In the situation when $\gcd(m,n)$ is a prime, we completely solve the problem.
Externí odkaz:
http://arxiv.org/abs/1406.6713
Publikováno v:
In BBA - Reviews on Cancer January 2021 1875(1)
Autor:
Stępień, Zofia, Szymaszkiewicz, Lucjan
An arc in $\Z^2_n$ is defined to be a set of points no three of which are collinear. We describe some properties of arcs and determine the maximum size of arcs for some small $n$.
Externí odkaz:
http://arxiv.org/abs/1512.02175