Results 171 to 180 of about 7,081,606 (216)

Cyclotomic Splitting Fields

Canadian Mathematical Bulletin, 1982
AbstractLet D be a division algebra whose class [D] is in B(K), the Brauer group of an algebraic number field K. If [D⊗KL] is the trivial class in B(L), then we say that L is a splitting field for D or L splits D. The splitting fields in D of smallest dimension are the maximal subfields of D.
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Cyclotomic fields are generated by cyclotomic Hecke L-values of totally real fields

Advances in Mathematics, 2022
Let \(K\) be a totally real number field \(K\), let \(p\ge3\) be an unramified prime and let \(H_p(K)\) be the \(p\)-part of the class-group (in the strict sense) of \(K\). For a character \(\chi\) of \(H_p(K)\) of the form \(\chi(X) = \psi(N_{K/\mathbb Q}(X))\), where \(\psi\) is a Dirichlet character mod \(p^n\) let \(L_K(s;\xi)\) be the ...
Jun, Byungheup, Lee, Jungyun, Sun, Hae-sang   +2 more
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Canonical bases for cyclotomic fields

Applicable Algebra in Engineering, Communication and Computing, 1990
Der Autor konstruiert eine Ganzheitsbasis des \(n\)-ten Kreiskörpers \(\mathbb{Q}^{(n)}\), welche für jedes \(d\mid n\) eine Ganzheitsbasis von \(\mathbb{Q}^{(d)}\) als Teilsystem enthält.
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On Some Invariants of Cyclotomic Fields

American Journal of Mathematics, 1958
where A, u and v are integers independent of n, The numbers A and a seem to have deep significance for the arithmetic of the fields Kn. In general, if the invariant 1 ,u(Kf/F) of a so-called r-extension K over a finite algebraic number field F is 0, then the Galois group of the maximal unramified abelian p-extension over K is, up to a finite subgroup ...
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CYCLOTOMIC FIELDS AND MODULAR CURVES

Russian Mathematical Surveys, 1971
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The cyclotomic fields

2021
IV SAYKLOTOMİK ALANLARDAKİ L-FONKSIYONLARI İsmail KOCAMEŞE Yüksek Lisans Tezi - Matematik Ocak 2005 Tez Yöneticisi: Prof. Dr. Barış KENDİRLİ ÖZ Bu çalışmada Dirihlet L-fonksiyonları ele alınmıştır. Bunun yanı sıra, sayklotomik alanlar çalışılmıştır. Ayrıca, genel L-fonksiyonları ve saylotomik alanlardaki L-fonksiyonları çalışılmıştır. Anahtar Kelimeler:
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Integral Bases for Subfields of Cyclotomic Fields

Applicable Algebra in Engineering, Communication and Computing, 1997
The standard integral basis \(B_n = \{1, \zeta, \ldots, \zeta^{\phi(n)-1}\}\) for the field of \(n\)-th roots of unity does not have the property that \(B_m \subset B_n\) for \(m \mid n\). \textit{W. Bosma} [Appl. Algebra Eng. Commun. Comput. 1, 125-134 (1990; Zbl 0741.11041)] has constructed integral bases with this property.
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Cyclotomic Fields as Abelian Fields

1998
For each positive integer m the cyclotomic field of the m-th roots of unity is easily seen to be an abelian field and indeed we have the following more detailed results.
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Quadratic and Cyclotomic Fields

1979
Ian Stewart, David Tall
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Regular Cyclotomic Fields

1998
Let l be an odd prime number and k (ζ) the cyclotomic field generated by = ζ = e 2πi/l is called a regular cyclotomic field and l is called a regular prime number if the number of ideal classes of the field k (ζ) is not divisible by l. The remaining chapters will be concerned exclusively with regular cyclotomic fields and with Kummer fields derived ...
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