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Cyclotomic Fields and Zeta Values
, 2006 Cyclotomic fields have occupied a central place in number theory, and the so called ""main conjecture"" on cyclotomic fields is arguably the deepest theorem known about them.
Coates, John, Sujatha, R
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MONOGENEITY IN CYCLOTOMIC FIELDS
International Journal of Number Theory, 2010A number field is said to be monogenic if its ring of integers is a simple ring extension ℤ[α] of ℤ. It is a classical and usually difficult problem to determine whether a given number field is monogenic and, if it is, to find all numbers α that generate a power integral basis {1, α, α2, …, αk} for the ring.
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Cyclotomic fields are generated by cyclotomic Hecke L-values of totally real fields
Advances in Mathematics, 2022Let \(K\) 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 +2 more
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On Some Invariants of Cyclotomic Fields
American Journal of Mathematics, 1958where 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, 1971zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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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Cyclotomic Fields as Abelian Fields
1998For 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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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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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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