Index form equations in sextic fields: a hard computation

Yuri Bilu; István Gaál; Kálmán Győry

Displaying similar documents to “Index form equations in sextic fields: a hard computation”

Power integral bases in the family of simplest quartic fields.

Olajos, Péter (2005)

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Power integral bases in orders of composite fields.

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

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An infinite family of totally real number fields

Humio Ichimura, Fuminori Kawamoto (2003)

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

István Gaál, Gábor Petrányi (2014)

Czechoslovak Mathematical Journal

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It is a classical problem in algebraic number theory to decide if a number field is monogeneous, that is if it admits power integral bases. It is especially interesting to consider this question in an infinite parametric family of number fields. In this paper we consider the infinite parametric family of simplest quartic fields $K$ generated by a root $ξ$ of the polynomial $P_{t} (x) = x^{4} - t x^{3} - 6 x^{2} + t x + 1$ , assuming that $t > 0$ , $t \neq 3$ and $t^{2} + 16$ has no odd square factors. In addition to generators of power integral bases we also calculate...