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arXiv · 1910.12105

Geometry of Biquadratic and Cyclic Cubic Log-Unit Lattices

Fernando Azpeitia Tellez·Christopher Powell·Shahed Sharif
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Abstract

By Dirichlet's Unit Theorem, under the log embedding the units in the ring of integers of a number field form a lattice, called the log-unit lattice. We investigate the geometry of these lattices when the number field is a biquadratic or cyclic cubic extension of $\mathbb{Q}$. In the biquadratic case, we determine when the log-unit lattice is orthogonal. In the cyclic cubic case, we show that the log-unit lattice is always equilateral triangular.

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Fernando Azpeitia Tellez, Christopher Powell, Shahed Sharif. 2019-10-26. Geometry of Biquadratic and Cyclic Cubic Log-Unit Lattices. https://arxiv.org/abs/1910.12105

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