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A cyclotomic field is a number field obtained by adjoining a complex primitive root of unity to $\mathbb Q$, the field of rational numbers.

9 votes
1 answer
231 views

Are the class numbers of $\mathbb{Q}(\cos(2\pi / m))$ $O(m^n)$ for some fixed $n$?

Question: Are the class numbers of $\mathbb{Q}(\cos(\frac{2\pi}m))$ $O(m^n)$ for some fixed $n$? Evidences (e.g. a recent paper) showing that the question above is open are also OK. Remark: If such $n …
1 vote
0 answers
219 views

Regulator of number fields of a special form

Is it possible to estimate the regulator of a number field of a special form (e.g. cyclotomic fields)? My motivation mainly comes from the investigation of the number fields $K_n=\mathbb{Q}[x]/(x^n+x …