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

This number theory-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Algebraic number theory Cyclotomic fields Number theory stubs Wikimedia Foundation. 2010. Игры ⚽ Поможем написать курсовую Fulvio Valbusa Skarpåker Stone Look at other dictionaries: Dirichlet's unit theorem — In mathematics, Dirichlet s unit theorem is a basic result in algebraic number theory due to Gustav Lejeune Dirichlet.[1] It determines the rank of the group of units in the ring OK of algebraic integers of a number field K. The regulator is a… …   Wikipedia Elliptic unit — In mathematics, elliptic units are certain units of abelian extensions of imaginary quadratic fields constructed using singular values of modular functions. They were introduced by Gilles Robert in 1973, and were used by John Coates and Andrew… …   Wikipedia List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia Root of unity — The 5th roots of unity in the complex plane In mathematics, a root of unity, or de Moivre number, is any complex number that equals 1 when raised to some integer power n. Roots of unity are used in many branches of mathematics, and are especially …   Wikipedia Class number formula — In number theory, the class number formula relates many important invariants of a number field to a special value of its Dedekind zeta function Contents 1 General statement of the class number formula 2 Galois extensions of the rationals 3 A …   Wikipedia Cubic field — In mathematics, specifically the area of algebraic number theory, a cubic field is an algebraic number field of degree three. Contents 1 Definition 2 Examples 3 Galois closure 4 …   Wikipedia Proofs of quadratic reciprocity — In the mathematical field of number theory, the law of quadratic reciprocity, like the Pythagorean theorem, has lent itself to an unusual number of proofs. Several hundred proofs of the law of quadratic reciprocity have been found.Proofs that are …   Wikipedia Algebraic number field — In mathematics, an algebraic number field (or simply number field) F is a finite (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector… …   Wikipedia Cubic reciprocity — is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x3 ≡ p (mod q) is solvable; the word reciprocity comes from the form of the main theorem, which states that …   Wikipedia Graduate Texts in Mathematics — (GTM) is a series of graduate level textbooks in mathematics published by Springer Verlag. The books in this series, like the other Springer Verlag mathematics series, are small yellow books of a standard size. This particular series is easily… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”