The Fifteen Theorem for Universal Hermitian Lattices over Imaginary Quadratic Fields

2007/10/26 by Byeong Moon Kim, Ji Young Kim, Kim, Byeong Moon +3
Computer Science · Mathematics · #11E20 #11E39 (Primary) #11E41 (Secondary) #Advanced Algebra and Geometry #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11E20 #msc:11E39 #msc:11E41

paper · pdf · doi:10.48550/arxiv.0710.4991

20 Pages

openalex publication_date 2007/10/26 · arxiv created 2008/12/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We will introduce a method to get all universal Hermitian lattices over imaginary quadratic fields over ℚ(√(-m)) for all m. For each imaginary quadratic field ℚ(√(-m)), we obtain a criterion on universality of Hermitian lattices: if a Hermitian lattice L represents 1, 2, 3, 5, 6, 7, 10, 13,14 and 15, then L is universal. We call this the fifteen theorem for universal Hermitian lattices. Note that the difference between Conway-Schneeberger's fifteen theorem and ours is the number 13.

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