Mordell-Weil lattices in characteristic 2. III: A Mordell-Weil lattice of rank 128.

Elkies, Noam D.

Displaying similar documents to “Mordell-Weil lattices in characteristic 2. III: A Mordell-Weil lattice of rank 128.”

Another 80-dimensional extremal lattice

Mark Watkins (2012)

Journal de Théorie des Nombres de Bordeaux

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We show that the unimodular lattice associated to the rank 20 quaternionic matrix group ${SL}_{2} (F_{41}) \otimes {\tilde{S}}_{3} \subset {GL}_{80} (Z)$ 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 simple groups) provides one proof that this lattice is distinct from the previous three, while computing the inner...

Rank frequencies for quadratic twists of elliptic curves.

Rubin, Karl, Silverberg, Alice (2001)

Experimental Mathematics

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The strongly perfect lattices of dimension $10$

Gabriele Nebe, Boris Venkov (2000)

Journal de théorie des nombres de Bordeaux

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This paper classifies the strongly perfect lattices in dimension $10$ . There are up to similarity two such lattices, $K_{10}^{'}$ and its dual lattice.

A note on the figure of merit of 2-dimensional rank 2 lattice rules.

Dick, Josef, Pillichshammer, Friedrich (2005)

Integers

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Finite atomistic lattices that can be represented as lattices of quasivarieties

K. Adaricheva, Wiesław Dziobiak, V. Gorbunov (1993)

Fundamenta Mathematicae

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We prove that a finite atomistic lattice can be represented as a lattice of quasivarieties if and only if it is isomorphic to the lattice of all subsemilattices of a finite semilattice. This settles a conjecture that appeared in the context of [11].