Geodesic
Type One Functions and Voronoï's Theorem
Journal of convex analysis, Tome 18 (2011) no. 2, pp. 341-351

Voir la notice de l'article provenant de la source Heldermann Verlag

Voronoï's theorem characterizes local maxima of the Hermite invariant m / det1/n defined on the open cone of positive definite n by n symmetric matrices, where m denotes the arithmetical minimum function. In this paper, we extend Voronoï's theorem to functions of the form m / ϕ when ϕ is a type one function. Moreover, we study the Hermite like constant defined from m / ϕ. 
@article{JCA_2011_18_2_JCA_2011_18_2_a1,
     author = {K. Sawatani and T. Watanabe},
     title = {Type {One} {Functions} and {Vorono{\"\i}'s} {Theorem}},
     journal = {Journal of convex analysis},
     pages = {341--351},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2011},
     url = {http://geodesic.mathdoc.fr/item/JCA_2011_18_2_JCA_2011_18_2_a1/}
}
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K. Sawatani; T. Watanabe. Type One Functions and Voronoï's Theorem. Journal of convex analysis, Tome 18 (2011) no. 2, pp. 341-351. http://geodesic.mathdoc.fr/item/JCA_2011_18_2_JCA_2011_18_2_a1/