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2007 Lenstra's Constant and Extreme Forms in Number Fields
R. Coulangeon, M. I. Icaza, M. O'Ryan
Experiment. Math. 16(4): 455-462 (2007).


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.


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R. Coulangeon. M. I. Icaza. M. O'Ryan. "Lenstra's Constant and Extreme Forms in Number Fields." Experiment. Math. 16 (4) 455 - 462, 2007.


Published: 2007
First available in Project Euclid: 6 March 2008

zbMATH: 1170.11019
MathSciNet: MR2378486

Primary: 11H55

Keywords: extreme forms , Humbert forms

Rights: Copyright © 2007 A K Peters, Ltd.

Vol.16 • No. 4 • 2007
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