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Results tagged with nt.number-theory
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user 34180
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
4
votes
Hypersurface missing just one point
An even further generalisation of this result is the Alon-Füredi theorem, which says that if a polynomial $f$ does not vanish completely on the "grid" $S = S_1 \times \dots \times S_n$ where $S_i$'s a …
- 1,197
14
votes
1
answer
797
views
Theorems proved using combinatorial nullstellensatz that have no other known proof
Alon's (or Alon and Tarsi's?) combinatorial nullstellensatz is a powerful algebraic tool with many applications in combinatorics and number theory. See this, this, this and this mathoverflow question. …
- 1,197
10
votes
Proofs of the Chevalley-Warning Theorem
For Chevalley's theorem, i.e., number of common zeroes not being one, any new proof of the following Lemma would give a 'new' proof.
Lemma Let $P \in \mathbb{F}_q[x_1, \ldots, x_n]$ such that $P(a …
- 1,197
10
votes
How to recognise that the polynomial method might work
I would like to add some more examples and references for the so called polynomial method that can help us recognise when it can be applied.
From what I understand so far, the polynomial method fall …
- 1,197