Cyclotomic Units

  • Lawrence C. Washington
Part of the Graduate Texts in Mathematics book series (GTM, volume 83)


The determination of the unit group of an algebraic number field is rather difficult in general. However, for cyclotomic fields, it is possible to give explicitly a group of units, namely the cyclotomic units, which is of finite index in the full unit group. Moreover, this index is closely related to the class number, a fact which allows us to prove Leopoldt’s p-adic class number formula. Finally, we study more closely the units of the pth cyclotomic field, and give relations with p-adic L-functions and with Vandiver’s conjecture.


Prime Ideal Finite Index Full Group Real Unit Algebraic Number Field 
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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Lawrence C. Washington
    • 1
  1. 1.Mathematics DepartmentUniversity of MarylandCollege ParkUSA

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