5
votes
1answer
210 views

The angular distribution of the $(a,b)$ in $p = a^2+b^2$, and the distribution of the lattices corresponding to prime ideals

Here is a really basic question which I wished I understood better about the primes of the Gaussian field $\mathbb{Z}[i]$. But I was curious about the possibility of generalizing it to other (real ...
4
votes
2answers
286 views

When does a dyadic prime ramify in a relative quadratic extension?

In a quadratic extension $\mathbb{Q}(\sqrt{d})$of $\mathbb{Q}$ it is clear that 2 ramifies if and only if $d\equiv 2,3\mod 4$ (easy to see if you compute the discriminant). But if I take a relative ...
2
votes
1answer
143 views

Independence of Chebotarev densities

I would appreciate a reference to the following statement, which, I was having an impression, is known: Let $L, M$ be field extensions of finite degree of a number field $K$, such that $L \cap M = ...