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...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.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 12171223)the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2021A1515010396)。
文摘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.
