Geometry of Biquadratic and Cyclic Cubic Log-Unit Lattices

2019/10/26 by Tellez, Fernando Azpeitia, Powell, Christopher, Sharif, Shahed · 2 citations
#11H06 #11R27 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1910.12105

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 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.

Cited by

• Classification of totally real number fields via their zeta function, regulator, and log unit lattice
• An improved upper bound on the covering radius of the logarithmic lattice of ℚ(ζ_n)

Related

• Families of Cyclic Cubic Fields
• Shapes of unit lattices in D_p-number fields
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• Unit lattices of D₄-quartic number fields with signature (2,1)
• Constructions of lattices via biquadratic and triquadratic fields