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pro vyhledávání: '"Martinet, Jacques"'
Autor:
Martinet, Jacques
We construct Euclidean lattices whose sets of minimal vectors support some large equiangular families of lines, using notably reduction modulo~$2$ of lattices. %as considered in \cite{Ma1} and \cite{Ma2}. We also consider some related problems, and a
Externí odkaz:
http://arxiv.org/abs/2403.09446
We enumerate the low dimensional cells in the Voronoi cell complexes attached to the modular groups $SL_N(Z)$ and $GL_N(Z)$ for $N=8,9,10,11$, using quotient sublattices techniques for $N=8,9$ and linear programming methods for higher dimensions. The
Externí odkaz:
http://arxiv.org/abs/1910.11598
Autor:
Martinet, Jacques
We compare for an $n$-dimensional Euclidean lattice $\Lb$ the smallest possible values of the product of the norms of $n$~vectors which either constitute a basis for $\Lb$ (Hermite-type inequalities) or are merely assumed to be independent (Minkowski
Externí odkaz:
http://arxiv.org/abs/1403.1457
Autor:
Martinet, Jacques
Let $\Lb$ be a lattice in an $n$-dimensional Euclidean space $E$ and let $\Lb'$ be a Minkowskian sublattice of $\Lb$, that is, a sublattice having a basis made of representatives for the Minkowski successive minima of $\Lb$. We consider the set of po
Externí odkaz:
http://arxiv.org/abs/1202.2295
Autor:
Martinet, Jacques, Schürmann, Achill
Publikováno v:
International Journal of Number Theory, 8 (2012), 551-564
We prove that all Euclidean lattices of dimension $n\le 9$ which are generated by their minimal vectors, also possess a basis of minimal vectors. By providing a new counterexample, we show that this is not the case for all dimensions $n\ge 10$.
Externí odkaz:
http://arxiv.org/abs/1105.5889
Publikováno v:
Mathematics of Computation, 81 (2012), 1063-1092
Let $\Lambda$ be a lattice in an $n$-dimensional Euclidean space $E$ and let $\Lambda'$ be a Minkowskian sublattice of $\Lambda$, that is, a sublattice having a basis made of representatives for the Minkowski successive minima of $\Lambda$. We extend
Externí odkaz:
http://arxiv.org/abs/0904.3110
Autor:
MARTINET, Jacques
Publikováno v:
Journal de Théorie des Nombres de Bordeaux, 2008 Jan 01. 20(2), i-xi.
Externí odkaz:
https://www.jstor.org/stable/43974407
Publikováno v:
Mathematics of Computation, 2012 Apr 01. 81(278), 1063-1092.
Externí odkaz:
https://www.jstor.org/stable/23267986
Autor:
BERGÉ, Anne-Marie, MARTINET, Jacques
Publikováno v:
Journal de Théorie des Nombres de Bordeaux, 2005 Jan 01. 17(2), 455-465.
Externí odkaz:
https://www.jstor.org/stable/43974346