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Results tagged with nt.number-theory
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user 4790
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
56
votes
5
answers
9k
views
How do we know that Fermat wrote his famous note in 1637?
It is widely stated that Fermat wrote his famous note on sums of powers ("Fermat's last theorem") in, or around, 1637. How do we know the date, if the note was only discovered after his death, in 1665 …
- 4,280
10
votes
Accepted
Subgroups of algebraic groups
The functor of injective homomorphisms from $H$ to $G$ is represented by a scheme of finite type over $\mathbb Z$ (a locally closed subscheme of the product $G^H$). If this has points over $\overline{ …
- 27k
1
vote
8
votes
Accepted
A criterion for freeness over a local ring
No, this is false as soon as $n ≥ 3$. A second syzygy $M$ of the residue field $K$ gives a counterexample: each $M[1/X_i]$ is projective, hence free, and it is reflexive, so the second condition is sa …
- 27k
5
votes
Analytical predicate for integers over complex numbers
Given any set $S$ of complex numbers without accumulation points, you can find an entire function with $S$ as its set of zeroes (this is known as Weierstrass's theorem). So the answer to your question …
- 27k
17
votes
To what extent is it true that "number theory = mathematics"?
I guess that the title is meant to be provocative: can anyone really believe that number theory is all of mathematics? "Number theory is all of mathematics" is equally false as "Category theory is all …
- 27k