On n-ADC integral quadratic lattices over algebraic number fields

2023/06/01 by Zilong He, He, Zilong
Computer Science · Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2306.00334

openalex publication_date 2023/06/01 · openalex created_date 2023/06/04 · openalex updated_date 2026/07/28

Abstract

In the paper, we extend the ADC property to the representation of quadratic lattices by quadratic lattices, which we define as n -ADC-ness. We explore the relationship between n-ADC-ness, n -regularity and n -universality for integral quadratic lattices. Also, for n≥ 2 , we give necessary and sufficient conditions for an integral quadratic lattice over arbitrary non-archimedean local fields to be n -ADC. Moreover, we show that over any algebraic number field F , an integral O_F -lattice with rank n+1 is n-ADC if and only if it is O_F-maximal of class number one.

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