On classic $n$-universal quadratic forms over dyadic local fields

TL;DR

This paper characterizes the conditions and minimal testing sets for classic n-universal quadratic forms over dyadic local fields, advancing understanding of their representation properties in local number theory.

Contribution

It provides a complete characterization and minimal testing sets for classic n-universal quadratic forms over dyadic local fields, a previously unexplored area.

Findings

Established equivalent conditions for classic n-universal forms.

Identified minimal testing sets for these forms.

Enhanced understanding of quadratic form representations over dyadic fields.

Abstract

Let $ n $ be an integer and $ n\ge 2 $. A classic integral quadratic form over local fields is called classic $ n $-universal if it represents all $n$-ary classic integral quadratic forms. We determine the equivalent conditions and minimal testing sets for classic $ n $-universal quadratic forms over dyadic local fields.