Kyoungmin Kim

activity

20152025

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11 papers · 1 filter

math.NT2025

Composition laws of binary quadratic forms and isolations of quadratic forms

Jangwon Ju, Daejun Kim, Kyoungmin Kim +2

A positive definite and integral quadratic form $f$ is called irrecoverable if there is a quadratic form $F$ such that it represents all proper subforms of $f$ , whereas it does not…

math.NT2023

Isolations of the sum of two squares from its proper subforms

Jangwon Ju, Daejun Kim, Kyoungmin Kim +2

For a (positive definite and integral) quadratic form $f$ , a quadratic form is said to be {\it an isolation of $f$ from its proper subforms} if it represents all proper subforms of…

math.NT2022

Primitively universal quaternary quadratic forms

Jangwon Ju, Daejun Kim, Kyoungmin Kim +2

A (positive definite and integral) quadratic form $f$ is said to be $universal$ if it represents all positive integers, and is said to be $primitively universal$ …

math.NT2020

Minimal universality criterion sets on the representations of quadratic forms

Kyoungmin Kim, Jeongwon Lee, Byeong-Kweon Oh

For a set $S$ of (positive definite and integral) quadratic forms with bounded rank, a quadratic form $f$ is called $S$ -universal if it represents all quadratic forms in $S$ . A sub…

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

Quadratic forms with a strong regularity property on the representations of squares

Kyoungmin Kim, Byeong-Kweon Oh

A (positive definite and non-classic integral) quadratic form is called strongly $s$ -regular if it satisfies a strong regularity property on the number of representations of square…

math.NT2019

The number of representations of squares by integral quaternary quadratic forms

Kyoungmin Kim

Let $f$ be a positive definite (non-classic) integral quaternary quadratic form. We say $f$ is strongly $s$ -regular if it satisfies a regularity property on the number of represent…

math.NT2018

A sum of squares not divisible by a prime

Kyoungmin Kim, Byeong-Kweon Oh

Let $p$ be a prime. We define $S (p)$ the smallest number $k$ such that every positive integer is a sum of at most $k$ squares of integers that are not divisible by $p$ . In this art…

math.NT2016

Spinor representations of positive definite ternary quadratic forms

Jangwon Ju, Kyoungmin Kim, Byeong-Kweon Oh

For a positive definite integral ternary quadratic form $f$ , let $r (k, f)$ be the number of representations of an integer $k$ by $f$ . The famous Minkowski-Siegel formula implies tha…

math.NT2016

The number of representations of squares by integral ternary quadratic forms (II)

Kyoungmin Kim, Byeong-Kweon Oh

Let $f$ be a positive definite ternary quadratic form. We assume that $f$ is non-classic integral, that is, the norm ideal of $f$ is $\z$. We say $f$ is {\it strongly $s$ -regular }…

math.NT2015

The number of representations of squares by integral ternary quadratic forms

Kyoungmin Kim, Byeong-Kweon Oh

Let $f$ be a positive definite integral ternary quadratic form and let $r (k, f)$ be the number of representations of an integer $k$ by $f$ . In this article we study the number of re…