Cyclotomic unit

In mathematics, a cyclotomic unit (or circular unit) is a unit of an algebraic number field which is the product of numbers of the form (ζa
n − 1) for ζ
n an n root of unity and 0 < a < n. Note that if n is the power of a prime ζa
n − 1 itself is not a unit; however the numbers (ζa
n − 1)/(ζ
n − 1) for (a, n) = 1, and ±ζa
n generate the group of cyclotomic units in this case (n power of a prime).

单词	Cyclotomic unit
释义	Cyclotomic unit 英语百科 Cyclotomic unit In mathematics, a cyclotomic unit (or circular unit) is a unit of an algebraic number field which is the product of numbers of the form (ζa n − 1) for ζ n an n root of unity and 0 < a < n. Note that if n is the power of a prime ζa n − 1 itself is not a unit; however the numbers (ζa n − 1)/(ζ n − 1) for (a, n) = 1, and ±ζa n generate the group of cyclotomic units in this case (n power of a prime).
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