On Washington group of circular units of some composita of quadratic fields
Michal Bulant (2005)
Mathematica Slovaca
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Michal Bulant (2005)
Mathematica Slovaca
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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.
Antonín Dvořák, David Jedelský, Juraj Kostra (1999)
Mathematica Slovaca
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John Myron Masley (1978)
Compositio Mathematica
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Kuniaki Horie (1990)
Compositio Mathematica
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Keiji Okano (2006)
Acta Arithmetica
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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.
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...