Cyclotomic unit

In mathematics, a cyclotomic unit is a unit of an algebraic number field of the form (ζⁿ − 1)/(ζ − 1) for ζ a root of unity, or more generally a unit that can be written as a product of these and a root of unity.

The cyclotomic units form a subgroup of finite index in the group of units of a cyclotomic field. In the case of prime power conductor this index is the class number of the maximal real subfield of the cyclotomic field.

See also

• Elliptic unit

References

• Serge Lang Cyclotomic Fields I and II ISBN 0-387-96671-4 Springer Verlag Dec 1, 1989
• Lawrence C. Washington Introduction to Cyclotomic Fields ISBN 0-387-94762-0 Springer Dec 1, 1996