Ternary quadratic forms representing all perfect squares except for 1.
| 구분 | 정수론 |
|---|---|
| 일정 | 2025-10-31 11:00 ~ 12:00 |
| 강연자 | Jangwon Ju (Korea National University of Education) |
| 기타 | |
| 담당교수 | 김도형 |
시간: 10월31일(금) 11시-12시
장소: 27동325호
Name : Jangwon Ju
Affiliation : Korea National University of Education
Title : Ternary quadratic forms representing all perfect squares except for 1.
Abstract : A positive definite integral quadratic form f is called irrecoverable if there exists a quadratic form F that represents all proper subforms of f , but does not represent f itself. In this case, F is called an isolation of f . In this talk, we introduce some recent results related to isolations of quadratic forms. Furthermore, we discuss ternary isolations of the unary quadratic form x 2 . We prove that there are at most 301 positive definite integral ternary quadratic forms that represent all perfect squares except for 1. Moreover, among them, we prove that 152 ternary quadratic forms are isolations of the unary quadratic form x 2 . This is a joint work with Daejun Kim, Kyoungmin Kim, Mingyu Kim and Byeong-Kweon Oh.
