Skip to main content
added 36 characters in body
Source Link
danseetea
  • 954
  • 2
  • 9
  • 17

Are there non-isomorphic number fields (say of the same degree and signature) that have the same discriminant and regulator? I'm guessing the answer is no - why?

And are therefocusing on fields of small degree (n=3 and n=4), what about a less restrictive question: can we find two such fields that just have the same regulator (no discriminant restrictions)? I'm guessing the answer is yes - can't think of an example.

Are there non-isomorphic number fields (say of the same degree and signature) that have the same discriminant and regulator? I'm guessing the answer is no - why?

And are there fields that just have the same regulator (no discriminant restrictions)? I'm guessing the answer is yes - can't think of an example.

Are there non-isomorphic number fields (say of the same degree and signature) that have the same discriminant and regulator? I'm guessing the answer is no - why?

And focusing on fields of small degree (n=3 and n=4), what about a less restrictive question: can we find two such fields that have the same regulator (no discriminant restrictions)?

Source Link
danseetea
  • 954
  • 2
  • 9
  • 17

Number fields with same discriminant and regulator?

Are there non-isomorphic number fields (say of the same degree and signature) that have the same discriminant and regulator? I'm guessing the answer is no - why?

And are there fields that just have the same regulator (no discriminant restrictions)? I'm guessing the answer is yes - can't think of an example.