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Results tagged with nt.number-theory
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user 15630
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
21
votes
What's the "best" proof of quadratic reciprocity?
There was some discussion above about how the proof with Gauss sums is hard to motivate. I disagree, but the motivation involves a little more (mild) algebraic number theory (i.e., Galois theory, alge …
- 1,890
11
votes
0
answers
1k
views
Linear algebra of elliptic curves over p-adic fields
Unfortunately, the following question is somewhat ill-posed. However, I hope to make what I'm looking for sufficiently clear.
Given two elliptic curves (or Abelian varieties) over $\mathbb{C}$, one c …
- 1,537
8
votes
l-adic Turrittin
Here's a naive formulation of an analogue, which is false. (This fits very well the conditional phrasing from your question, since it would be an analogue if it were true!)
Levelt-Turrittin says that …
- 1,537
4
votes
2
answers
544
views
Maps preserving algebraic numbers
Suppose $f:\mathbb{C}\to\mathbb{C}$ is a map with your favorite smoothness condition (say, $C^1, C^{\infty}$ or holomorphic) and suppose that $f(\overline{\mathbb{Q}})\subset\overline{\mathbb{Q}}$. Is …
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- 1