컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0209 |
|---|---|
| 분류(Section) | Special Session |
| 분과(Session) | (SS-01) Algebraic Number Theory and Related Topics (SS-01) |
| 발표시간(Time) | 20th-C-10:40 -- 11:10 |
| 영문제목 (Title(Eng.)) |
Minimal rank of primitively $n$-universal quadratic forms over local fields |
| 저자(Author(s)) |
Byeong-Kweon Oh1, Jongheun Yoon1 Seoul National University1 |
| 초록본문(Abstract) | For a prime $p$ and a positive integer $n$, an integral quadratic form over a ring $\mathbb{Z}_p$ is called primitively $n$-universal if it primitively represents all integral quadratic forms of rank $n$ over $\mathbb{Z}_p$. In 2021, Earnest and Gunawardana provided criteria to determine whether a given integral quadratic form over $\mathbb{Z}_p$ is primitively $1$-universal. In this talk, we prove that the minimal rank of primitively $n$-universal integral quadratic form over $\mathbb{Z}_p$ is $2n$, if $p$ is an odd prime or if $n$ is at least five. Moreover, we obtain a complete classification of primitively $2$-universal integral quadratic forms over $\mathbb{Z}_p$ of minimal rank. |
| 분류기호 (MSC number(s)) |
11E08, 11E20 |
| 키워드(Keyword(s)) | Primitive $n$-universality |
| 강연 형태 (Language of Session (Talk)) |
Korean |