منابع مشابه
Another 80-dimensional extremal lattice
We show that the unimodular lattice associated to the rank 20 quaternionic matrix group SL2(F41)⊗ S̃3 ⊂ GL80(Z) is a fourth example of an 80-dimensional extremal lattice. Our method is to use the positivity of the Θ-series in conjunction with an enumeration of all the norm 10 vectors. The use of Aschbacher’s theorem on subgroups of finite classical groups (reliant on the classification of finite...
متن کاملAnother 80 - dimensional extremal lattice par
We show that the unimodular lattice associated to the rank 20 quaternionic matrix group SL2(F41)⊗ S̃3 ⊂ GL80(Z) is a fourth example of an 80-dimensional extremal lattice. Our method is to use the positivity of the Θ-series in conjunction with an enumeration of all the norm 10 vectors. The use of Aschbacher’s theorem on subgroups of finite classical groups (reliant on the classification of finite...
متن کاملOn the Extremality of an 80-Dimensional Lattice
We show that a specific even unimodular lattice of dimension 80, first investigated by Schulze-Pillot and others, is extremal (i.e., the minimal nonzero norm is 8). This is the third known extremal lattice in this dimension. The known part of its automorphism group is isomorphic to SL2(F79), which is smaller (in cardinality) than the two previous examples. The technique to show extremality invo...
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We develop an algorithm computing the transcendental lattice and the Mordell–Weil group of an extremal elliptic surface. As an example, we compute the lattices of four exponentially large series of surfaces
متن کاملExtremal Ideals of the Lattice of Multisets
We present here constructions of ideals A of the poset of n-vectors (x1, ..., xn) with integer entries, ordered coordinatewise, on which the maximal and minimal values of Wφ(A) = ∑ x∈A φ( ∑n i=1 xi) are achieved for a given unimodal function φ. As a consequence we get a new approach to prove the well-known ClementsLindström Theorem [6].
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2012
ISSN: 1246-7405
DOI: 10.5802/jtnb.795