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Displaying 381 – 400 of 459

Torsion of the Witt group

M. Karoubi (1976)

Mémoires de la Société Mathématique de France

Trace functions and Galois invariant p-adic measures.

Marian Vajaitu, Alexandru Zaharescu (2006)

Publicacions Matemàtiques

Transcendence results on the generating functions of the characteristic functions of certain self-generating sets, II

Peter Bundschuh, Keijo Väänänen (2015)

Acta Arithmetica

This article continues a previous paper by the authors. Here and there, the two power series F(z) and G(z), first introduced by Dilcher and Stolarsky and related to the so-called Stern polynomials, are studied analytically and arithmetically. More precisely, it is shown that the function field ℂ(z)(F(z),F(z⁴),G(z),G(z⁴)) has transcendence degree 3 over ℂ(z). This main result contains the algebraic independence over ℂ(z) of G(z) and G(z⁴), as well as that of F(z) and F(z⁴). The first statement is...

Twisted Pfister forms.

Hoffmann, Detlev W. (1996)

Documenta Mathematica

Twists of Hessian Elliptic Curves and Cubic Fields

Katsuya Miyake (2009)

Annales mathématiques Blaise Pascal

In this paper we investigate Hesse’s elliptic curves $H_{μ} : U^{3} + V^{3} + W^{3} = 3 μ U V W, μ \in Q - {1}$ , and construct their twists, $H_{μ, t}$ over quadratic fields, and $\tilde{H} (μ, t), μ, t \in Q$ over the Galois closures of cubic fields. We also show that $H_{μ}$ is a twist of $\tilde{H} (μ, t)$ over the related cubic field when the quadratic field is contained in the Galois closure of the cubic field. We utilize a cubic polynomial, $R (t; X) : = X^{3} + t X + t, t \in Q - {0, - 27 / 4}$ , to parametrize all of quadratic fields and cubic ones. It should be noted that $\tilde{H} (μ, t)$ is a twist of $H_{μ}$ as algebraic curves because it may not always have any rational points...

Two remarks on the inverse Galois problem for intersective polynomials

Jack Sonn (2009)

Journal de Théorie des Nombres de Bordeaux

A (monic) polynomial $f (x) \in ℤ [x]$ is called intersective if the congruence $f (x) \equiv 0$ mod $m$ has a solution for all positive integers $m$ . Call $f (x)$ nontrivially intersective if it is intersective and has no rational root. It was proved by the author that every finite noncyclic solvable group $G$ can be realized as the Galois group over $ℚ$ of a nontrivially intersective polynomial (noncyclic is a necessary condition). Our first remark is the observation that the corresponding result for nonsolvable $G$ reduces to the ordinary...