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Results tagged with nt.number-theory
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user 5480
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
12
votes
Two questions about finiteness of ideal classes in abstract number rings
Here is an answer to your "question 0" - an example of an "exotic" number ring. (This should be a comment but it is too long.)
Construct a sequence of number rings $\mathbb{Z}=R_0\subset R_1\subset …
- 2,441
22
votes
who fixed the topology on ideles?
They are too old for Math Reviews, but I think the articles in question are:
Von Neumann: "Zur Prüferischen Theorie der idealen Zahlen", Acta Scientiarum Mathematicum (Szeged) 2:4 (1926) (can be rea …
- 2,441
13
votes
L'un des problèmes fondamentaux de la théorie des nombres
Although this isn't at the moment heading towards the Riemann hypothesis, the most promising line of research in this area seems to be Lichtenbaum's Weil-etale cohomology. In the 1951 paper you cite, …
- 2,441
29
votes
Accepted
Cusp forms and L^2
This is a long answer because the question asks quite a lot of things. I agree that Gelbart's book, although inspirational, is hard for someone without a strong analytic background. The Boulder and Co …
- 2,441
8
votes
Accepted
Mod l local Galois representations (l different from p)
The image of wild inertia is a finite $p$-group, and if $d$ is the degree of an irreducible representation of a $p$-group over an algebraically closed field of characteristic $\ne p$, then $d$ is a po …
- 2,441
15
votes
Accepted
integer solutions to quadratic forms
Here is the standard geometric argument: after extracting common factors, you are asking for rational points on the quadric $Q\colon x^2-w^2=z^2-y^2$ in $\mathbb{P}^3$, which is isomorphic to $\mathbb …
- 2,441