A new lower bound for Hermite's constant for symplectic lattices
| Autor: | Bjoern Muetzel |
|---|---|
| Přispěvatelé: | GTA, Institut de Mathématiques et de Modélisation de Montpellier (I3M), Centre National de la Recherche Scientifique (CNRS)-Université Montpellier 2 - Sciences et Techniques (UM2)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université Montpellier 2 - Sciences et Techniques (UM2)-Université de Montpellier (UM), Swiss National Science Foundation |
| Jazyk: | angličtina |
| Rok vydání: | 2011 |
| Předmět: |
Hermite's constant
Geometry of numbers High Energy Physics::Lattice symplectic lattices 11H56 11H60 and 58D19 01 natural sciences Upper and lower bounds Combinatorics Mathematics - Algebraic Geometry 11H56 11H60 58D19 0103 physical sciences FOS: Mathematics 0101 mathematics symmetric lattices Algebraic Geometry (math.AG) Circulant matrix Mathematics Algebra and Number Theory Hermite polynomials 010102 general mathematics Multiplicative function patterned matrices [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] Matrix group 010307 mathematical physics Constant (mathematics) Symplectic geometry |
| Zdroj: | International Journal of Number Theory International Journal of Number Theory, World Scientific Publishing, 2012, 8 (4), pp.1067-1080. ⟨10.1142/S1793042112500637⟩ |
| ISSN: | 1793-0421 |
| DOI: | 10.1142/S1793042112500637⟩ |
| Popis: | In section 1 we give an improved lower bound on Hermite's constant $\delta_{2g}$ for symplectic lattices in even dimensions ($g=2n$) by applying a mean-value argument from the geometry of numbers to a subset of symmetric lattices. Here we obtain only a slight improvement. However, we believe that the method applied has further potential. In section 2 we present new families of highly symmetric (symplectic) lattices, which occur in dimensions of powers of two. Here the lattices in dimension $2^n$ are constructed with the help of a multiplicative matrix group isomorphic to $({\Z_2}^n,+)$. We furthermore show the connection of these lattices with the circulant matrices and the Barnes-Wall lattices. Comment: 13 pages |
| Databáze: | OpenAIRE |
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