On n-universal quadratic forms over dyadic local fields  

作　　者：Zilong He Yong Hu 

机构地区：[1]School of Computer Science and Technology,Dongguan University of Technology,Dongguan,523808,China [2]Department of Mathematics,Southern University of Science and Technology,Shenzhen,518055,China

出　　处：《Science China Mathematics》2024年第7期1481-1506,共26页中国科学（数学）（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No. 12171223);the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2021A1515010396)。

摘　　要：Let n≥2 be an integer. We give necessary and sufficient conditions for an integral quadratic form over dyadic local fields to be n-universal by using invariants from Beli's theory of bases of norm generators.Also, we provide a minimal set for testing n-universal quadratic forms over dyadic local fields, as an analogue of Bhargava and Hanke's 290-theorem(or Conway and Schneeberger's 15-theorem) on universal quadratic forms with integer coefficients.

关 键 词：integral quadratic forms n-universal quadratic forms dyadic fields 290-theorem 

分 类 号：O172.2[理学—数学]