Lenstra's Constant and Extreme Forms in Number Fields



Experimental Mathematics

Lenstra's Constant and Extreme Forms in Number Fields

R. Coulangeon, M. I. Icaza, and M. O'Ryan

Source: Experiment. Math. Volume 16, Issue 4 (2007), 455-462.

Abstract

In this paper we compute $\gamma_{K,2$ for $K=\mathbb{Q}(\rho)$, where $\rho$ is the real root of the polynomial $x^3 -x^2 +1 =0$. We refine some techniques introduced in Baeza, et al. to construct all possible sets of minimal vectors for perfect forms. These refinements include a relation between minimal vectors and the Lenstra constant. This construction gives rise to results that can be applied in several other cases.

Primary Subjects: 11H55
Keywords: Humbert forms; extreme forms

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.em/1204836515
Mathematical Reviews number (MathSciNet): MR2378486


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