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Results tagged with nt.number-theory
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user 44293
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
3
votes
2
answers
632
views
Practical use of estimates for the Gauss Circle Problem
This question is related to this and this ones. The Gauss Circle problem asks for the number $N(r)$ of integer points within a sphere of radius $r$ centered at the origin. It is well known that $N(r) …
- 800
8
votes
2
answers
527
views
Integer numbers of the form $m = x^n + y^n$
First of all, I am no number theorist, so this question may be a little dummy.
The two squares theorem imply that $m = x^2 + y^2$ for some (possible zero) integer numbers $x,y$ iff $m$ factors as $m = …
- 800
4
votes
1
answer
1k
views
regulators of number fields
Related question: Totally real number fields with bounded regulators
Given a number field $K$ with degree $n$ and determinant $D$, what is the "best" upper bound for its regulator $R$, if any? I know …
- 800
2
votes
Accepted
Covolume of the row span of a matrix and of the kernel of a matrix
Equality (2) can be proved through the Smith Normal Form of $A$. I am pretty sure there is a simpler proof then the one below.
One can decompose $A$ into: $A = U D V^t$ where $D = ( \hat{D}\,\, \left …
- 800
3
votes
1
answer
343
views
Indefinite Ternary Forms with Square Discriminant
Is there any general theory to find the numbers represented by ternary forms of the type
$q(x,y,z)=ax^2+bx^2-abz^2,$
when $a,b$ are prime?
By doing an internet search, the closest I found was the …
- 800
5
votes
What fraction of the integer lattice can be seen from the origin?
The two-dimensional version of this question was already asked (although in a different language) here.
In fact, besides the generalization to measurable sets mentioned by Pete, this result can be ge …
- 800