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Results tagged with nt.number-theory
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user 461
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
8
votes
Accepted
When matrices commute
(1) Let $A$ be a commutative ring, and let $M$ and $N$ be $A$-modules. If the natural morphism from $A$ to $\text{End}_A(M\oplus N)$ is surjective, then the annihilators of $M$ and $N$ are comaximal. …
- 4,416
1
vote
How would one even begin to try to prove that a simple number-theoretic statement is undecid...
EDIT
Here is my problem. To prove that statement S is undecidable is to
(1) prove that one cannot prove S.
I think I understand the meaning of the second "prove". (It depends of course on the cont …
- 4,416
11
votes
Galois theory timeline
EDIT. Here is the part of the answer that has been rewritten:
We give below a short proof of the Fundamental Theorem of Galois Theory (FTGT) for finite degree extensions. We derive the FTGT from two …
- 4,416
9
votes
Applications of the Chinese remainder theorem
The Chinese Remainder Theorem gives a way to compute matrix exponentials.
Indeed, let $A$ be a complex square matrix, put $B:=\mathbb C[A]$. This is a Banach algebra, and also a $\mathbb C[X]$-algeb …
2
votes
Shortest/Most elegant proof for $L(1,\chi)\neq 0$
I know it's not an answer to the question, but rather another (probably naive) question suggested by the original question.
It seems to me that proving the prime number theorem for arithmetic progres …
- 4,416