PENCILS OF NORM FORM EQUATIONS AND A CONJECTURE OF THOMAS

AbstractThe results herein continue observations on norm form equations and continued fractions begun and continued in the works [1]−[3], and [5]−[6].

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A one-way function based on norm form equations

Periodica Mathematica Hungarica ◽

10.1023/b:mahu.0000040535.45427.38 ◽

2004 ◽

Vol 49 (1) ◽

pp. 1-13 ◽

Cited By ~ 8

Author(s):

Attila Bérczes ◽

J. Ködmön ◽

Attila Pethő

Keyword(s):

Norm Form ◽

One Way Function

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ON THE SQUARE-FREE REPRESENTATION FUNCTION OF A NORM FORM AND NILSEQUENCES

Journal of the Institute of Mathematics of Jussieu ◽

10.1017/s1474748015000389 ◽

2015 ◽

Vol 17 (1) ◽

pp. 107-135 ◽

Cited By ~ 1

Author(s):

Lilian Matthiesen

Keyword(s):

Recent Work ◽

Rational Points ◽

Representation Function ◽

Norm Form ◽

Free Representation

We show that the restriction to square-free numbers of the representation function attached to a norm form does not correlate with nilsequences. By combining this result with previous work of Browning and the author, we obtain an application that is used in recent work of Harpaz and Wittenberg on the fibration method for rational points.

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On Algebraic Groups Defined by Norm Forms of Separable Extensions

Nagoya Mathematical Journal ◽

10.1017/s0027763000002002 ◽

1957 ◽

Vol 11 ◽

pp. 125-130 ◽

Cited By ~ 1

Author(s):

Takashi Ono

Keyword(s):

Vector Space ◽

Algebraic Group ◽

Algebraic Groups ◽

The Other ◽

Linear Transformations ◽

Finite Degree ◽

Separable Extension ◽

Norm Form ◽

Multiplicative Groups ◽

Separable Extensions

Let K be any field, and L a separable extension of K of finite degree. L has a structure of vector space over K, and we shall denote this space by V. The space of endomorphisms of V will be denoted by Let x be any element of L, and N(x) the norm of x relative to the extension L/K. N is then a function defined on V with values in K. We shall call N the norm form on V. The multiplicative groups of non-zero elements of K and L will be denoted by K* and L* respectively. Let H be any subgroup of if K*. Then the elements z of L* such that N(z)∈H form a subgroup of L*, which we shall denote by GH. On the other hand the elements s of such that N(sx) = Λ(s)N(x) with Λ(s)∈H for all X∈V, form obviously a subgroup of GL(V), which we shall denote by becomes an algebraic group if H=K* or {1}. In case will mean the group of linear transformations of V leaving semi-invariant the norm form of L/K and in case will mean the group of linear transformations of V leaving invariant the norm form of L/K.

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