Algebraic systems of quadratic forms of number fields and function fields.

Martin Krüskemper

Displaying similar documents to “Algebraic systems of quadratic forms of number fields and function fields.”

Class fields towers of imaginary quadratic fields.

Robert Gold, James R. Brink (1986/87)

Manuscripta mathematica

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Infinite 2-class field towers of some imaginary quadratic number fields

Yutaka Sueyoshi (2004)

Acta Arithmetica

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Systems of quadratic forms

Albrecht Pfister (1979)

Mémoires de la Société Mathématique de France

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Representability by certain norm forms over algebraic number fields

John Smith (1975)

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Indivisibility of class numbers of imaginary quadratic function fields

Dongho Byeon (2008)

Acta Arithmetica

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Algorithms for quadratic forms over real function fields

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.

Some quartic number fields containing an imaginary quadratic subfield

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.