Search results

{{short description|Analogue of Stickelberger's theorem for real abelian fields}} ...theorem''' is an analogue of [[Stickelberger's theorem]] for real abelian fields, introduced by Francisco {{harvs|txt|last=Thaine|year=1988}}. Thaine's meth ...

...a's μ-invariant is 0 for cyclotomic extensions of abelian algebraic number fields}} ...invariant]] is zero for cyclotomic ''p''-adic extensions of abelian number fields. ...

...ical Society]], "for contributions to number theory, especially cyclotomic fields, and for mentoring at all levels".<ref>{{cite web|url=http://www.ams.org/cg Washington wrote a standard work on [[cyclotomic field]]s. He also worked on [[p-adic]] [[L-function]]s. He wrote a treatise ...

| fields= | thesis_title=Coeflicients in the cyclotomic polynomial for numbers with at most three distinct odd primes in their fact ...

...th>, the only <math>\mathbb{Z}_p</math>-extension of <math>F</math> is the cyclotomic one (since it is totally real). ...cyclotomic extensions of <math>k</math>, one can define a tower of number fields ...

Examples of monogenic fields include: * [[Quadratic fields]]: ...

...d Complexities of Cyclotomic Fast Fourier Transforms Over Arbitrary Finite Fields| journal=IEEE Transactions on Signal Processing|volume=60|issue=3|year=2012 ...h>\{0, 1, 2, \ldots, N-1\}</math> can be partitioned into <math>l+1</math> cyclotomic cosets modulo <math>N</math>: ...

This is an incomplete list of [[number fields]] with class number 1. It is believed that there are infinitely many such number fields, but this has not been proven.<ref name="neu"/> ...

In [[mathematics]], a '''tower of fields''' is a sequence of [[field extension]]s A tower of fields may be finite or [[infinite sequence|infinite]]. ...

In [[number theory]], a '''cyclotomic field''' is a [[number field]] obtained by [[adjunction (field theory)|adjo ...t was in the process of his deep investigations of the arithmetic of these fields (for [[prime number|prime]]&nbsp;{{mvar|n}})&nbsp;– and more precisely, bec ...

Let <math>L/K</math> be a finite Galois extension of global fields with Galois group <math>G</math>. Then the [[discriminant of an algebraic n ...math>L = \mathbf{Q}(\zeta_{p^n})/\mathbf{Q}</math> be a [[cyclotomic field|cyclotomic extension]] of the rationals. The Galois group <math>G</math> equals <math> ...

...vide a versatile set of tools for computing the Galois cohomology of local fields. ...et '''Q'''_''p''(1) denote the [[cyclotomic character|''p''-adic cyclotomic character]] of ''G_K'' (i.e. the [[Tate module]] of μ). A [[Galoi ...

...ic L-function|''p''-adic ''L''-functions]] and [[ideal class group]]s of [[cyclotomic field]]s, proved by [[Kenkichi Iwasawa]] for primes satisfying the [[Kummer ...roved other generalizations of the main conjecture for imaginary quadratic fields.{{sfn|Manin|Panchishkin|2007|p=246}} ...

===Cyclotomic units=== The [[cyclotomic unit]]s satisfy ''distribution relations''. Let ''a'' be an element of ''' ...

| fields = [[Mathematics]] ...category in which Morava E-theories play the role of algebraically closed fields.<ref>{{cite arXiv |last1=Burklund |first1=Robert |last2=Schlank |first2=Tom ...

...and [[algebraic number theory]] (Stickelberger relation in the theory of [[cyclotomic field]]s). ...also yields information about the structure of the [[class group]] of a [[cyclotomic field]] as a module over its abelian [[Galois group]] (cf [[Iwasawa theory] ...

...ok |last1=Washington |first1=Lawrence C. |title=Introduction to Cyclotomic Fields |date=1997 |publisher=Springer |page=372 |edition=2}}</ref> ...=Srivastav | first4=Anupam | title=Swan modules and Hilbert–Speiser number fields | journal=Journal of Number Theory | volume=79 | pages=164–173 | doi=10.100 ...

...ly, certain [[Galois module]]s over [[tower of fields|towers of cyclotomic fields]] or even more general towers. A ''p''-adic ''L''-function arising in this ==Totally real fields== ...

...he ''p''-adic regulator. As a consequence, Leopoldt's conjecture for those fields is equivalent to their ''p''-adic Dedekind zeta functions having a simple p ...on | last1=Brumer | first1=Armand | title=On the units of algebraic number fields | doi=10.1112/S0025579300003703 | mr=0220694 | year=1967 | journal=[[Mathem ...

...d Davenport]] and [[Hans Heilbronn]] computed the asymptotic for all cubic fields {{harv|Davenport|Heilbronn|1971}}.</ref> ...to the rational number field '''Q'''. Such fields are always complex cubic fields since each positive number has two [[complex number|complex]] non-real cube ...