Zobrazeno 1 - 10
of 5 345
pro vyhledávání: '"Small generators"'
Autor:
Widmer, Martin
We show that for each abelian number field $K$ of sufficiently large degree $d$ there exists an element $\alpha\in K$ with $K=\IQ(\alpha)$ and absolute Weil height $H(\alpha)\ll_d |\Delta_K|^{1/2d}$ , where $\Delta_K$ denotes the discriminant of $K$.
Externí odkaz:
http://arxiv.org/abs/2312.02044
Let $K$ be an algebraic number field and $H$ the absolute Weil height. Write $c_K$ for a certain positive constant that is an invariant of $K$. We consider the question: does $K$ contain an algebraic integer $\alpha$ such that both $K = \mathbb{Q}(\a
Externí odkaz:
http://arxiv.org/abs/2307.11849
Akademický článek
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Autor:
CHU, MICHELLE, LI, HAN
Publikováno v:
Proceedings of the American Mathematical Society, 2016 Dec 01. 144(12), 5121-5127.
Externí odkaz:
https://www.jstor.org/stable/procamermathsoci.144.12.5121
Autor:
Vaaler, Jeffrey D., Widmer, Martin
Publikováno v:
Math. Proc. Camb. Phil. Soc. 159 (2015) 379-385
Let $D>1$ be an integer, and let $b=b(D)>1$ be its smallest divisor. We show that there are infinitely many number fields of degree $D$ whose primitive elements all have relatively large height in terms of $b$, $D$ and the discriminant of the number
Externí odkaz:
http://arxiv.org/abs/1410.5258
Autor:
Widmer, Martin
Publikováno v:
J. Theor. Nombres Bordeaux 22, (2010), no. 3, 544-551
Let $K/k$ be a finite extension of a global field. Such an extension can be generated over $k$ by a single element. The aim of this article is to prove the existence of a "small" generator in the function field case. This answers the function field v
Externí odkaz:
http://arxiv.org/abs/1204.4158
Autor:
WIDMER, Martin
Publikováno v:
Journal de Théorie des Nombres de Bordeaux, 2010 Jan 01. 22(3), 747-753.
Externí odkaz:
https://www.jstor.org/stable/43973052
Autor:
Chinburg, Ted, Stover, Matthew
Let $k$ be a number field, suppose that $B$ is a central simple division algebra over $k$, and choose any maximal order $\mathcal{D}$ of $B$. The object of this paper is to show that the group $\mathcal{D}_S^*$ of $S$-units of $B$ is generated by ele
Externí odkaz:
http://arxiv.org/abs/1204.5968
Publikováno v:
Mathematics of Computation, 2008 Apr 01. 77(262), 1185-1197.
Externí odkaz:
https://www.jstor.org/stable/40234551
Autor:
Ruppert, Wolfgang M.
This is a revised version of ANT-0045. If K is a number field of degree n with discriminant D, if K=Q(a) then H(a)>c(n)|D|^(1/(2n-2)) where H(a) is the height of the minimal polynomial of a. We ask if one can always find a generator a of K such that
Externí odkaz:
http://arxiv.org/abs/math/9612229