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Results tagged with nt.number-theory
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user 717
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
12
votes
Learning Class Field Theory: Local or Global First?
Perhaps no one else will share my opinion but I am a fan of Neukirch's approach to both local and global class field theory as presented in his book on algebraic number theory. Neukirch constructs an …
- 5,243
1
vote
Definition of elementary number theory
I refine my answer: I think that problems in elementary number theory can be characterized as problems in number theory for which both the problem and its solution can be understood in a fair amount o …
1
vote
1
answer
1k
views
Neukirch's class field axiom and cohomology of units for unramified extension
This question may be too detailed but perhaps somebody knows the answer: Neukirch proofs in his algebraic number theory book in Chapter IV, Proposition 6.2, that his class field axiom implies that the …
- 5,243
5
votes
Global fields: What exactly is the analogy between number fields and function fields?
From the valuation theoretic point of view both types of fields (nearly) look the same. If we compare Q with Fp[X], then the set of all (real-valued) absolute values on these fields is made up by the …
- 5,243