Daejun Kim

collaborators

4 papers

math.NT2020

Prime-universal diagonal quadratic forms

Jangwon Ju, Daejun Kim, Kyoungmin Kim +2

A (positive definite and integral) quadratic form is said to be $prime-universal$ if it represents all primes. Recently, Doyle and Williams in [2] classified all prime-uni…

math.NT2019

Representations of finite number of quadratic forms with same rank

Daejun Kim, Byeong-Kweon Oh

Let $m, n$ be positive integers with $m \leq n$ . Let $κ (m, n)$ be the largest integer $k$ such that for any (positive definite and integral) quadratic forms $f_{1}, \dots, f_{k}$ of rank $…

math.NT2019

A sum of three nonunit squares of integers

Daejun Kim, Jeongwon Lee, Byeong-Kweon Oh

We say a positive integer is a sum of three nonunit squares if it is a sum of three squares of integers other than one. In this article, we find all integers which are sums of thre…

math.NT2019

On a quadratic Waring's problem with congruence conditions

Daejun Kim

For each positive integer $n$ , let $g_{Δ} (n)$ be the smallest positive integer $g$ such that every complete quadratic polynomial in $n$ variables which can be represented by a sum of…