Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1982 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Washington, L.C. (1982). Cyclotomic Units. In: Introduction to Cyclotomic Fields. Graduate Texts in Mathematics, vol 83. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0133-2_8
Download citation
DOI: https://doi.org/10.1007/978-1-4684-0133-2_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-0135-6
Online ISBN: 978-1-4684-0133-2
eBook Packages: Springer Book Archive