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Let $ε$ be an algebraic unit of the degree $n \geq 3$ . Assume that the extension $ℚ (ε) / ℚ$ is Galois. We would like to determine when the order $ℤ [ε]$ of $ℚ (ε)$ is $Gal (ℚ (ε) / ℚ)$ -invariant, i.e. when the $n$ complex conjugates $ε_{1}, \dots, ε_{n}$ of $ε$ are in $ℤ [ε]$ , which amounts to asking that $ℤ [ε_{1}, \dots, ε_{n}] = ℤ [ε]$ , i.e., that these two orders of $ℚ (ε)$ have the same discriminant. This problem has been solved only for $n = 3$ by using an explicit formula for the discriminant of the order $ℤ [ε_{1}, ε_{2}, ε_{3}]$ . However, there is no known similar formula for $n > 3$ . In the present paper, we put forward and motivate three...

Why is the class number of $ℚ (\sqrt[3]{11})$ even?

F. Lemmermeyer (2013)

Mathematica Bohemica

In this article we will describe a surprising observation that occurred in the construction of quadratic unramified extensions of a family of pure cubic number fields. Attempting to find an explanation will lead us on a magical mystery tour through the land of pure cubic number fields, Hilbert class fields, and elliptic curves.

Displaying 141 – 150 of 150

Ueber die Anzahl der Idealklassen in reinen kubischen Zahlkörpern.

Units generating the ring of integers of complex cubic fields

Units in parametrized p-adatropic number fields

Units in some parametric families of quartic fields

?Verstümmelte" Grundeinheiten für biquadratische und bikubische Zahlkörper.

When is the order generated by a cubic, quartic or quintic algebraic unit Galois invariant: three conjectures

Why is the class number of $ℚ (\sqrt[3]{11})$ even?

Zur Berechnung der Kapitualtion in bikubischen Zahlkörpern.

Арифметические свойства трехмерных алгебраических торов

О представлении прямой суммы двух квадратичных полей рациональными симметрическими матрицами

Currently displaying 141 – 150 of 150