Lenstra's Constant and Extreme Forms in Number Fields
Coulangeon, R. ; Icaza, M. I. ; O'Ryan, M.
Experiment. Math., Tome 16 (2007) no. 1, p. 455-462 / Harvested from Project Euclid
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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.
Publié le : 2007-05-15
Classification:  Humbert forms,  extreme forms,  11H55 
@article{1204836515,
     author = {Coulangeon, R. and Icaza, M. I. and O'Ryan, M.},
     title = {Lenstra's Constant and Extreme Forms in Number Fields},
     journal = {Experiment. Math.},
     volume = {16},
     number = {1},
     year = {2007},
     pages = { 455-462},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1204836515}
}

Coulangeon, R.; Icaza, M. I.; O'Ryan, M. Lenstra's Constant and Extreme Forms in Number Fields. Experiment. Math., Tome 16 (2007) no. 1, pp.  455-462. http://gdmltest.u-ga.fr/item/1204836515/