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Results tagged with nt.number-theory
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user 14371
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
11
votes
6
answers
4k
views
Examples of Using Class Field Theory
I'm trying to learn class field theory and I'm wondering if anyone knows of any good sources with a bunch of examples on how to actually use it? This can be anything from books to course notes to cour …
- 263
7
votes
3
answers
3k
views
Techniques for computing fundamental units in cubic extensions
Are there any slick ways of computing the fundamental unit for the cubic polynomial of the form $X^3+aX+b$ over $\mathbb{Q}$? The simplest example would be $X^3+X-1$, where a root $\alpha$ is a unit w …
- 263
3
votes
2
answers
423
views
Implications of a relation on algebraic numbers
Assume that $\alpha_1,\ldots,\alpha_n$ are algebraic numbers. Assuming that
$\sum_{i=1}^n \alpha_i^k \in \mathbb{Z}$
for all $k\in\mathbb{N}$. Does this imply that the $\alpha_i$ are actually algebr …
- 263