Seminar

Abstracts : For a positive integer n, a positive definite integral quadratic form is called primitively n-universal if it primitively represents all positive definite integral quadratic forms of rank n. Ju, Kim, Kim, Kim, and Oh proved that there are exactly 107 primitively 1-universal quaternary quadratic forms up to isometry. In this talk, we prove that the minimal rank of a primitively 2-universal integral quadratic form is six, and we prove that there are exactly 201 primitively 2-universal senary integral quadratic forms up to isometry. This is joint work with Prof. Byeong-Kweon Oh.