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Étant donnés $F$ un corps commutatif de caractéristique $2$ , $γ_{1}, γ_{2}$ des formes bilinéaires d’Albert et $π_{1}, π_{2}$ des $k$ -formes quadratiques de Pfister, ou $γ_{1}, γ_{2}$ des $k$ -formes bilinéaires de Pfister et $π_{1}, π_{2}$ des formes quadratiques d’Albert (resp. $γ_{1}, γ_{2}$ des formes bilinéaires d’Albert et $π_{1}, π_{2}$ des $k$ -formes bilinéaires de Pfister avec la condition que $γ_{i} \otimes π_{i}$ , $i = 1, 2$ , soient anisotropes), alors on montre que $γ_{1} \otimes π_{1} ⊥ γ_{2} \otimes π_{2} \in I_{q}^{k + 3} F$ (resp. $I^{k + 3} F$ ) si et seulement si $γ_{1} \otimes π_{1}$ est semblable à $γ_{2} \otimes π_{2}$ . Un exemple montre que la condition de l’anisotropie est nécessaire dans le cas bilinéaire....

Simultaneous diagonal inequalities of odd degree.

T. Nadesalingam, Jane Pitman (1989)

Journal für die reine und angewandte Mathematik

Simultaneous p-adic Zeros of Quadratic Forms.

Wolfgang M. Schmidt (1980)

Monatshefte für Mathematik

Simultaneous quadratic equations II

R. Cook (1973)

Acta Arithmetica

Simultaneous quadratic inequalities

R. Cook (1974)

Acta Arithmetica

Singer-Zyklen in klassischen Gruppen.

Bertram Huppert (1970)

Mathematische Zeitschrift

Skew-Symmetric Vanishing Lattices and Their Monodromy Groups.

W.A.M. Janssen (1984)

Mathematische Annalen

Skew-Symmetric Vanishing Lattices and Their Monodromy Groups. II.

W.A.M. Janssen (1985)

Mathematische Annalen

Small zeros of hermitian forms over a quaternion algebra

Wai Kiu Chan, Lenny Fukshansky (2010)

Acta Arithmetica

Small zeros of quadratic forms over algebraic function fields

Albrecht Pfister (1997)

Acta Arithmetica

Solution to a Problem of Lubelski and an Improvement of a Theorem of His

A. Schinzel (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

The paper consists of two parts, both related to problems of Lubelski, but unrelated otherwise. Theorem 1 enumerates for a = 1,2 the finitely many positive integers D such that every odd positive integer L that divides x² +Dy² for (x,y) = 1 has the property that either L or $2^{a} L$ is properly represented by x²+Dy². Theorem 2 asserts the following property of finite extensions k of ℚ : if a polynomial f ∈ k[x] for almost all prime ideals of k has modulo at least v linear factors, counting multiplicities,...

Some algebraic aspects of quadratic forms over fields of characteristic two.

Baeza, Ricardo (2001)

Documenta Mathematica

Some applications of decomposable form equations to resultant equations

K. Győry (1993)

Colloquium Mathematicae

1. Introduction. The purpose of this paper is to establish some general finiteness results (cf. Theorems 1 and 2) for resultant equations over an arbitrary finitely generated integral domain R over ℤ. Our Theorems 1 and 2 improve and generalize some results of Wirsing [25], Fujiwara [6], Schmidt [21] and Schlickewei [17] concerning resultant equations over ℤ. Theorems 1 and 2 are consequences of a finiteness result (cf. Theorem 3) on decomposable form equations over R. Some applications of Theorems...

Some aspects of Gaussian composition

Gordon Pall (1973)

Acta Arithmetica

Some estimates for diagonal equations over p-adic fields

M. Dodson (1982)

Acta Arithmetica

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