Class fields towers of imaginary quadratic fields.
Robert Gold, James R. Brink (1986/87)
Manuscripta mathematica
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Robert Gold, James R. Brink (1986/87)
Manuscripta mathematica
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Yutaka Sueyoshi (2004)
Acta Arithmetica
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Albrecht Pfister (1979)
Mémoires de la Société Mathématique de France
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John Smith (1975)
Acta Arithmetica
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Dongho Byeon (2008)
Acta Arithmetica
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Konrad Jałowiecki, Przemysław Koprowski (2016)
Banach Center Publications
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This paper presents algorithms for quadratic forms over a formally real algebraic function field K of one variable over a fixed real closed field k. The algorithms introduced in the paper solve the following problems: test whether an element is a square, respectively a local square, compute Witt index of a quadratic form and test if a form is isotropic/hyperbolic. Finally, we remark on a method for testing whether two function fields are Witt equivalent.
Stéphane R. Louboutin (2011)
Colloquium Mathematicae
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Let ε be a quartic algebraic unit. We give necessary and sufficient conditions for (i) the quartic number field K = ℚ(ε) to contain an imaginary quadratic subfield, and (ii) for the ring of algebraic integers of K to be equal to ℤ[ε]. We also prove that the class number of such K's goes to infinity effectively with the discriminant of K.
Craig Cordes, John Ramsey (1978)
Fundamenta Mathematicae
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Dress, Andreas W.M. (1997)
Beiträge zur Algebra und Geometrie
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L. Szczepanik (1978)
Colloquium Mathematicae
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Winfried Scharlau (1987)
Mathematische Zeitschrift
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Yoonjin Lee (2006)
Acta Arithmetica
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Toru Komatsu (2001)
Acta Arithmetica
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V. Sprindžuk (1974)
Acta Arithmetica
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Kostadinka Lapkova (2012)
Acta Arithmetica
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