Results 91 to 100 of about 130 (120)
Chromatic cyclotomic extensions
Geometry and TopologyWe construct Galois extensions of the T(n)-local sphere, lifting all finite abelian Galois extensions of the K(n)-local sphere. This is achieved by realizing them as higher semiadditive analogues of cyclotomic extensions. Combining this with a general form of Kummer theory, we lift certain elements from the K(n)-local Picard group to the T(n)-local ...
Tomer Schlank
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On the defining polynomials of maximal real cyclotomic extensions
Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas, 2008 Summary: The aim of this paper is to show that the simplest techniques of linear algebra allow us to make explicit the defining equations of the maximal real cyclotomic extensions \(\mathbb Q(\zeta+\zeta^ {-1})\) of \(\mathbb Q(\zeta)\), where \(\zeta\) stands for a primitive \(p^ \nu\)-th root of unity with \(p\) a rational prime and \(\nu\) any ...
A Arenas
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Cyclotomic Units in Zp-Extensions
Journal of Algebra, 1995 Kucera, R., Nekovar, J.
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l-Extensions of CM-fields and cyclotomic invariants
Journal of Number Theory, 1980 AbstractThe Hurwitz type relation of Iwasawa's λ−-invariants in l-extensions of CM-fields is given under the assumption of the vanishing of μ−-invariants.
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Cyclotomic Z2-extensions of J-fields
Journal of Number Theory, 1982 AbstractHurwitz-type relations of Iwasawa's λ2−-invariants and the 2-ranks of the “narrow” ideal class groups in the 2-extensions of J-fields are given under the assumption of the vanishing of μ2-invariants.
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Cyclotomic units in z p -extensions
Israel Journal of Mathematics, 1991LetK0 be the maximal real subfield of the field generated by thep-th root of 1 over ℚ, andK∞ be the basic Zp-extension ofK0 for a fixed odd primep. LetKn be itsn-th layer of this tower. For eachn, we denote the Sylowp-subgroup of the ideal class group ofKn byAn, and that ofEnCn byBn, whereEn (resp.Cn) is the group of units (resp. cyclotomic units ofKn.
Jae Moon Kim, Sunghan Bae, In-Sok Lee
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ON GALOIS EXTENSIONS OF A MAXIMAL CYCLOTOMIC FIELD
Mathematics of the USSR-Izvestiya, 1980This paper is devoted to the realization of certain types of Chevalley groups as the Galois group of extensions of certain cyclotomic fields. In addition, a criterion for an algebraic curve to be defined over an algebraic number field is given. Bibliography: 11 titles.
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An extension of binary cyclotomic sequences having order 2lt
Discrete Mathematics, Algorithms and Applications, 2022Several reasonably cyclotomic sequences are constructed by cyclotomic classes having good pseudo-randomness property. In this paper, we derive the linear complexity of an extended binary cyclotomic sequences of order [Formula: see text] over finite field having period [Formula: see text].
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2001
In this chapter we shall describe the work of Gauss and Lagrange on the resolution by radicals of cyclotomic polynomials. Then we will describe some of the work of Jacobi and Kummer on the ideal theory of rings of cyclotomic integers.
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In this chapter we shall describe the work of Gauss and Lagrange on the resolution by radicals of cyclotomic polynomials. Then we will describe some of the work of Jacobi and Kummer on the ideal theory of rings of cyclotomic integers.
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A primality test using cyclotomic extensions
1989The cyclotomic polynomial Φs(x) (where s is an integer >1) is the irreducible polynomial over ℚ, having the primitive s-th roots of unity as zeroes. If \(\mathbb{K}\) is the field ℚ or \(\mathbb{F}_p\), with p a prime, an s-th cyclotomic extension of \(\mathbb{K}\) is the splitting field of Φs(x) over \(\mathbb{K}\).
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