0
votes
0answers
60 views

existence of elements with specific norms in pure cubic fields

Is there any specific way to find an element with a given norm in pure cubic field? say for an example an element of norm 5 in pure (monogenic) cubic field of 11. it is easy to check that 5 as an ...
3
votes
1answer
251 views

Distribution of associate primes modulo q in number fields

In Dirichlet's theorem for number fields, I asked about an analogue of Dirichlet's theorem (or I guess I should call it the Prime Number Theorem for Arithmetic Progressions) for number fields. ...
5
votes
1answer
833 views

Dirichlet's theorem for number fields

I'd like to see a formulation of Dirichlet's theorem for number fields, i.e. some analogue of the assertion: The number of primes less than $N$ congruent to $a \pmod{m}$ where $(a,m)=1$ is ...
12
votes
5answers
1k views

Families of number fields of prime discriminant

When I am testing conjectures I have about number fields, I usually want to control the ramification, especially minimize to a single prime with tame ramification. Hence, I usually look for fields of ...