Abstract
A classical theorem of Minkowski and Hlawka states that there exists a lattice in \({\mathbb{R}^n}\) with packing density at least \({2^{1-n}}\). Buser and Sarnak proved the analogue of this result in the context of complex abelian varieties. Here we give an improvement of this analogue; this shows a conjecture of Muetzel.
Résumé
Un théorème classique de Minkowski et Hlawka montre l’existence d’un réseau de \({\mathbb{R}^n}\) à densité d’empilement \({\ge 2^{1-n}}\). Buser et Sarnak ont établi l’analogue de ce résultat dans le cadre des variétés abéliennes complexes. On donne ici une amélioration de cet analogue; cela prouve une conjecture de Muetzel.
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