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Results tagged with nt.number-theory
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user 13947
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
1
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answers
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Elementary Number Theory
Assume we have a free ring $S$ of rank 2 and $K= S \otimes Q$. Now if we define an equivalent relation similar to the case $S=O_{K}$ then is it true that the $S$-ideal classes form a group ?
- 463
4
votes
0
answers
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Higher Composition laws
I can not understand the definition of balanced triple $(I_1,I_2,I_3)$ in a Dedekind Domain which is defined in the Higher composition laws I of Manjul Bhargava.
I would be so thankful if somebody c …
- 463
3
votes
1
answer
1k
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Hilbert class field of Quadratic fields
Is there any method to find the Hilbert Class field of quadratic fields? Is there any bound for their dimensions? For example, if $4|d-1$ then $Q(\sqrt{d},i)$ is contained in the Hilbert class field o …
- 463
14
votes
4
answers
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$Q(\sqrt{2})=Q((\sqrt{2}+1)^n)$
Observe that we have $Q(\sqrt{2})=Q((\sqrt{2}+1)^n)$.
More generally, assume that $K$ is a finite extension of Q. Is there any $\alpha \in K$ such that $K=Q(\alpha^n)$ for every $n \in N$?
- 463