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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.
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"multi-dimensional" cyclotomic number
Let $F_q$ be the finite field with $q$ elements with characteristic $p$ and with $g$ being a primitive root. Let $N$ be a divisor of $q-1$ and let $C_0$ be the subgroup of $F_q^*$ with index $N$. Then …