The Resolution of Norm Form Equations

2019 ◽  
pp. 81-92
Author(s):  
István Gaál
Keyword(s):  
Norm Form

Continued Fractions, Jacobi Symbols, and Quadratic Diophantine Equations

2000 ◽  
Vol 43 (2) ◽  
pp. 218-225 ◽  
Author(s):  
R. A. Mollin ◽  
A. J. van der Poorten
Keyword(s):  
Continued Fractions ◽  
Diophantine Equations ◽  
Norm Form

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

scholarly journals A one-way function based on norm form equations

2004 ◽  
Vol 49 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Attila Bérczes ◽  
J. Ködmön ◽  
Attila Pethő
Keyword(s):  
Norm Form ◽  
One Way Function

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

2015 ◽  
Vol 17 (1) ◽  
pp. 107-135 ◽  
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.

scholarly journals On Algebraic Groups Defined by Norm Forms of Separable Extensions

1957 ◽  
Vol 11 ◽  
pp. 125-130 ◽  
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.

scholarly journals Arithmetic Progressions in the Solution Sets of Norm Form Equations

2010 ◽  
Vol 40 (2) ◽  
pp. 383-395 ◽  
Author(s):  
Attila Bérczes ◽  
Lajos Hajdu ◽  
Attila Pethő
Keyword(s):  
Arithmetic Progressions ◽  
Solution Sets ◽  
Norm Form

scholarly journals Norm form equations IV: Rational functions

Mathematika ◽  
1986 ◽  
Vol 33 (2) ◽  
pp. 204-211 ◽  
Author(s):  
R. C. Mason
Keyword(s):  
Rational Functions ◽  
Norm Form

scholarly journals THE NORM FORM OF A RATIONAL DIVISION ALGEBRA

1957 ◽  
Vol 43 (6) ◽  
pp. 506-509
Author(s):  
A. A. Albert
Keyword(s):  
Division Algebra ◽  
Norm Form

scholarly journals Integral points on norm-form varieties

1986 ◽  
Vol 24 (3) ◽  
pp. 272-283 ◽  
Author(s):  
B.Z. Moroz
Keyword(s):  
Integral Points ◽  
Norm Form

scholarly journals On the height of solutions to norm form equations

2018 ◽  
Vol 183 (4) ◽  
pp. 385-396
Author(s):  
Shabnam Akhtari ◽  
Jeffrey D. Vaaler
Keyword(s):  
Norm Form
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