Calculating all elements of minimal index in the infinite parametric family of simplest quartic fields

István Gaál; Gábor Petrányi

Displaying similar documents to “Calculating all elements of minimal index in the infinite parametric family of simplest quartic fields”

Power integral bases in the family of simplest quartic fields.

Olajos, Péter (2005)

Experimental Mathematics

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Computing all monogeneous mixed dihedral quartic extensions of a quadratic field

István Gaál, Gábor Nyul (2001)

Journal de théorie des nombres de Bordeaux

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Let $M$ be a given real quadratic field. We give a fast algorithm for determining all dihedral quartic fields $K$ with mixed signature having power integral bases and containing $M$ as a subfield. We also determine all generators of power integral bases in $K$ . Our algorithm combines a recent result of Kable [9] with the algorithm of Gaál, Pethö and Pohst [6], [7]. To illustrate the method we performed computations for $M = ℚ (\sqrt{2}), ℚ (\sqrt{3}), ℚ (\sqrt{5}) .$

O-minimal version of Whitney's extension theorem

Krzysztof Kurdyka, Wiesław Pawłucki (2014)

Studia Mathematica

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This is a generalized and improved version of our earlier article [Studia Math. 124 (1997)] on the Whitney extension theorem for subanalytic $^{p}$ -Whitney fields (with p finite). In this new version we consider Whitney fields definable in an arbitrary o-minimal structure on any real closed field R and obtain an extension which is a $^{p}$ -function definable in the same o-minimal structure. The Whitney fields that we consider are defined on any locally closed definable subset of Rⁿ. In such a...

Index form equations in sextic fields: a hard computation

Yuri Bilu, István Gaál, Kálmán Győry (2004)

Acta Arithmetica

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Power integral bases in orders of composite fields.

Gaál, István, Olajos, Péter, Pohst, Michael (2002)

Experimental Mathematics

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On the subfields of cyclotomic function fields

Zhengjun Zhao, Xia Wu (2013)

Czechoslovak Mathematical Journal

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Let $K = 𝔽_{q} (T)$ be the rational function field over a finite field of $q$ elements. For any polynomial $f (T) \in 𝔽_{q} [T]$ with positive degree, denote by $Λ_{f}$ the torsion points of the Carlitz module for the polynomial ring $𝔽_{q} [T]$ . In this short paper, we will determine an explicit formula for the analytic class number for the unique subfield $M$ of the cyclotomic function field $K (Λ_{P})$ of degree $k$ over $𝔽_{q} (T)$ , where $P \in 𝔽_{q} [T]$ is an irreducible polynomial of positive degree and $k > 1$ is a positive divisor of $q - 1$ . A formula for the analytic class...

On the Stark-Shintani units and the ideal class groups in the cyclotomic $ℤ_{p}$ -extensions of class fields over real quadratic fields

Tsuyoshi Itoh (2002)

Acta Arithmetica

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The Joly–Becker theorem for $*$ –orderings

Igor Klep, Dejan Velušček (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

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We prove the $*$ –version of the Joly–Becker theorem: a skew field admits a $*$ –ordering of level $n$ iff it admits a $*$ –ordering of level $n ℓ$ for some (resp. all) odd $ℓ \in ℕ$ . For skew fields with an imaginary unit and fields stronger results are given: a skew field with imaginary unit that admits a $*$ –ordering of higher level also admits a $*$ –ordering of level $1$ . Every field that admits a $*$ –ordering of higher level admits a $*$ –ordering of level $1$ or $2$