Number fields and discriminants (2/2)
Some interesting questions:
what is the minimum value of ∆K if [K : Q] = n? or for a given signature (r1, r2) ?
list all number fields K (up to isomorphism) such that ∆K ∈ [A, B] ?
as B → ∞, how many number fields with ∆K < B do we have ?
There are many variations where we fix the signature or restrict finite ramification, but Galois
actions must now be taken into account as they severely restrict possibilities. This requires refining
the question to a fixed Galois group for the Galois closure of K/Q. If needed, we can then
concatenate contributions of each group at the end.
PARI/GP day 2021 (02/06/2021) – p. 3/14