ON WELL-ROUNDED IDEAL LATTICES

DOI10.1142/S179304211250011XzbMath1292.11077arXiv1101.4442OpenAlexW1974770505MaRDI QIDQ3116596

Lenny Fukshansky, Kathleen L. Petersen

Publication date: 24 February 2012

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.4442

zbMATH Keywords

ideal latticequadratic number fieldsminimal vectorsWell-rounded lattice

Mathematics Subject Classification ID

Quadratic extensions (11R11) Lattices and convex bodies (number-theoretic aspects) (11H06) Cyclotomic extensions (11R18) Algebraic numbers; rings of algebraic integers (11R04) General binary quadratic forms (11E16)

Related Items (9)

Cyclic and well-rounded lattices ⋮ Well-rounded twists of ideal lattices from real quadratic fields ⋮ Well-rounded twists of ideal lattices from imaginary quadratic fields ⋮ The linear transformation that relates the canonical and coefficient embeddings of ideals in cyclotomic integer rings ⋮ Well-rounded algebraic lattices in odd prime dimension ⋮ ON WELL-ROUNDED IDEAL LATTICES II ⋮ On integral well-rounded lattices in the plane ⋮ A complete classification of well-rounded real quadratic ideal lattices ⋮ Stability of ideal lattices from quadratic number fields

Cites Work

• On well-rounded sublattices of the hexagonal lattice
• On the Euclidean minimum of some real number fields
• On similarity classes of well-rounded sublattices of \(\mathbb Z^2\)
• Upper bounds for Euclidean minima of algebraic number fields
• On distribution of well-rounded sublattices of \(\mathbb Z^2\)
• Arithmetic Progressions, Prime Numbers, and Squarefree Integers
• Algebraic lattice constellations: bounds on performance
• On the complexity of decoding lattices using the Korkin-Zolotarev reduced basis
• Minkowski’s conjecture, well-rounded lattices and topological dimension

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