Binary normal regular Hermitian lattices over imaginary quadratic fields

2007/10/26 by Byeong Moon Kim, Ji Young Kim, Kim, Byeong Moon +3
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.0710.4998

Abstract

We call a positive definite Hermitian lattice regular if it represents all integers which can be represented locally by the lattice. We investigate binary regular Hermitian lattices over imaginary quadratic fields ℚ(√(-m)) and provide a complete list of the (normal) Hermitian lattices.

Related

• Even universal binary Hermitian lattices over imaginary quadratic fields
• 2-universal Hermitian lattices over imaginary quadratic fields
• The Fifteen Theorem for Universal Hermitian Lattices over Imaginary Quadratic Fields
• An algorithm for g-invariant on unary Hermitian lattices over imaginary quadratic fields
• Simple proofs for universal binary Hermitian lattices