Multiplicative lattices in global fields

DOI10.1007/BF01231520zbMath0739.11024MaRDI QIDQ1177116

Michael A. Tsfasman, Michael Yu. Rosenbloom

Publication date: 26 June 1992

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143821

zbMATH Keywords

function fieldcongruence lattices\(S\)-unit groupsadditive number field latticesasymptotically good latticescongruence sublatticesdense sphere packingdensity exponentmultiplicative groups of global fieldsprincipal multiplicative latticestowers of algebraic number fields

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Class field theory (11R37) Lattice packing and covering (number-theoretic aspects) (11H31)

Related Items (13)

A note on short vectors in lattices from function fields ⋮ On the size of the Jacobians of curves over finite fields ⋮ A note on lattices of rational functions ⋮ Lattices with exponentially large kissing numbers ⋮ Lattices from Hermitian function fields ⋮ Euclidean minima of algebraic number fields ⋮ Maximal order codes over number fields ⋮ A Note on Lattice Packings via Lattice Refinements ⋮ Packing superballs from codes and algebraic curves ⋮ On the lattices from elliptic curves over finite fields ⋮ Linear codes with exponentially many light vectors ⋮ Small height in fields generated by singular moduli ⋮ Improvement on asymptotic density of packing families derived from multiplicative lattices

Cites Work

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• Holomorphic supergeometry and Yang-Mills superfields
• Constructive high-dimensional sphere packings
• An exhaustion bound for algebraic-geometric ``modular codes
• Tours de corps de classes et estimations de discriminants
• Modular curves, Shimura curves, and Goppa codes, better than Varshamov-Gilbert bound
• On extension of quadratic modules from affine to projective spaces
• On the product of the conjugates outside the unit circle of an algebraic number

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