On Washington group of circular units of some composita of quadratic fields
Michal Bulant (2005)
Mathematica Slovaca
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Displaying similar documents to “Completely normal elements in some finite abelian extensions”
On Washington group of circular units of some composita of quadratic fields
Generation of Hauptmoduln of Γ1(N) by Weierstrass units and application to class fields
Chang Kim, Ja Koo (2011)
Open Mathematics
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We show that the modular functions j 1,N generate function fields of the modular curve X 1(N), N ∈ {7; 8; 9; 10; 12}, and apply them to construct ray class fields over imaginary quadratic fields.
The fields of degree seven over rationals with a normal basis generated by a unit
Antonín Dvořák, David Jedelský, Juraj Kostra (1999)
Mathematica Slovaca
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Class numbers of real cyclic number fields with small conductor
John Myron Masley (1978)
Compositio Mathematica
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CM-fields with all roots of unity
Kuniaki Horie (1990)
Compositio Mathematica
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Abelian p-class field towers over the cyclotomic ℤₚ-extensions of imaginary quadratic fields
Keiji Okano (2006)
Acta Arithmetica
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A survey of computational class field theory
Henri Cohen (1999)
Journal de théorie des nombres de Bordeaux
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We give a survey of computational class field theory. We first explain how to compute ray class groups and discriminants of the corresponding ray class fields. We then explain the three main methods in use for computing an equation for the class fields themselves: Kummer theory, Stark units and complex multiplication. Using these techniques we can construct many new number fields, including fields of very small root discriminant.
Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory
Chipchakov, I. (2004)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20. This paper gives a characterization of Henselian discrete valued fields whose finite abelian extensions are uniquely determined by their norm groups and related essentially in the same way as in the classical local class field theory. It determines the structure of the Brauer groups and character groups of Henselian discrete valued strictly primary quasilocal (or PQL-) fields, and thereby, describes the forms...
Some results on local fields
Akram Lbekkouri (2013)
Annales UMCS, Mathematica
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Let K be a local field with finite residue field of characteristic p. This paper is devoted to the study of the maximal abelian extension of K of exponent p−1 and its maximal p-abelian extension, especially the description of their Galois groups in solvable case. Then some properties of local fields in general case are studied too.