Jangwon Ju

activity

20162025

most citedTernary universal sums of generalized polygonal numbers

4 citations · 8 across the 17 of their papers we have counts for

collaborators

18 papers

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.NT2024

Even universal sums of triangular numbers

Jangwon Ju

For an arbitrary integer $x$ , an integer of the form $T (x) = \frac{x ^{2} + x}{2}$ is called a triangular number. Let $α_{1}, \dots, α_{k}$ be positive integers. A sum $Δ_{α_1,\dots,α_k}(x_…

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.NT2022

Tight universal octagonal forms

Jangwon Ju, Mingyu Kim

Let $P_{8} (x) = 3 x^{2} - 2 x$ . For positive integers $a_{1}, a_{2}, \dots, a_{k}$ , a polynomial of the form $a_{1} P_{8} (x_{1}) + a_{2} P_{8} (x_{2}) + \dots + a_{k} P_{8} (x_{k})$ is called an octagonal form. For a positive i…

math.NT2022

Tight universal sums of $m$ -gonal numbers

Jangwon Ju, Mingyu Kim

For a positive integer $n$ , the set of all integers greater than or equal to $n$ is denoted by $T (n)$ . A sum of generalized $m$ -gonal numbers $g$ is called tight $\mathcal…

math.NT2022

Almost universal sums of triangular numbers with one exception

Jangwon Ju

For an arbitrary integer $x$ , an integer of the form $T (x) = \frac{x ^{2} + x}{2}$ is called a triangular number. For positive integers $α_{1}, α_{2}, \dots, α_{k}$ , a sum $Δ_{α_1,α_2,\dots,α_k}(x…

math.NT2020★ 1 cited

The pentagonal theorem of sixty-three and generalizations of Cauchy's lemma

Jangwon Ju, Daejun Kim

In this article, we study the representability of integers as sums of pentagonal numbers, where a pentagonal number is an integer of the form $P_{5} (x) = \frac{3 x ^{2} - x}{2}$ for some non…

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.NT2020

Ternary quadratic forms representing same integers

Jangwon Ju

In 1997, Kaplansky conjectured that if two positive definite ternary quadratic forms with integer coefficients have perfectly identical integral representations, then they are isom…

math.NT2018

Universal mixed sums of generalized $4$ - and $8$ -gonal numbers

Jangwon Ju, Byeong-Kweon Oh

An integer of the form $P_{m} (x) = \frac{( m - 2 ) x ^{2} - ( m - 4 ) x}{2}$ for an integer $x$ , is called a generalized $m$ -gonal number. For positive integers $α_{1}, \dots, α_{u}$ and $β_{1}, \dots, β_{v}$ ,…

math.NT2018

Universal sums of generalized pentagonal numbers

Jangwon Ju

For an integer $x$ , an integer of the form $P_{5} (x) = \frac{3 x ^{2} - x}{2}$ is called a generalized pentagonal number. For positive integers $α_{1}, \dots, α_{k}$ , a sum $Φ_{α_1,\dots,α_k}(x_1,x_…

math.NT2017

Universal sums of generalized octagonal numbers

Jangwon Ju, Byeong-Kweon Oh

An integer of the form $P_{8} (x) = 3 x^{2} - 2 x$ for some integer $x$ is called a generalized octagonal number. A quaternary sum $Φ_{a, b, c, d} (x, y, z, t) = a P_{8} (x) + b P_{8} (y) + c P_{8} (z) + d P_{8} (t)$ of ge…

math.NT2017★ 1 cited

A generalization of Gauss' triangular theorem

Jangwon Ju, Byeong-Kweon Oh

A quadratic polynomial $Φ_{a, b, c} (x, y, z) = x (a x + 1) + y (b y + 1) + z (cz + 1)$ is called universal if the diophantine equation $Φ_{a, b, c} (x, y, z) = n$ has an integer solution $x, y, z$ for any non n…

math.NT2016★ 4 cited

Ternary universal sums of generalized polygonal numbers

Jangwon Ju, Byeong-Kweon Oh, Bangnam Seo

An integer of the form $p_{m} (x) = \frac{( m - 2 ) x ^{2} - ( m - 4 ) x}{2} (m \geq 3)$ , for some integer $x$ is called a generalized polygonal number of order $m$ . A ternary sum $Φ_{i,j,k}^{a,b,c}(…

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

Genus-correspondences respecting spinor genus

Jangwon Ju, Byeong-Kweon Oh

For two positive definite integral ternary quadratic forms $f$ and $g$ and a positive integer $n$ , if $n \cdot g$ is represented by $f$ and $n \cdot d g = df$ , then the pair $(f, g)$ is…

math.NT2016★ 2 cited

A generalization of Watson transformation and representations of ternary quadratic forms

Jangwon Ju, Inhwan Lee, Byeong-Kweon Oh

Let $L$ be a positive definite (non-classic) ternary $\z$-lattice and let $p$ be a prime such that a $\frac 12\z_p$-modular component of $L_{p}$ is nonzero isotropic and $4 \cdot d L$ …

Composition laws of binary quadratic forms and isolations of quadratic forms

Even universal sums of triangular numbers

Isolations of the sum of two squares from its proper subforms

Primitively universal quaternary quadratic forms

Tight universal octagonal forms

Tight universal sums of m-gonal numbers

Almost universal sums of triangular numbers with one exception

The pentagonal theorem of sixty-three and generalizations of Cauchy's lemma

Prime-universal diagonal quadratic forms

Ternary quadratic forms representing same integers

Universal mixed sums of generalized 4- and 8-gonal numbers

Universal sums of generalized pentagonal numbers

Universal sums of generalized octagonal numbers

A generalization of Gauss' triangular theorem

Ternary universal sums of generalized polygonal numbers

Spinor representations of positive definite ternary quadratic forms

Genus-correspondences respecting spinor genus

A generalization of Watson transformation and representations of ternary quadratic forms

Tight universal sums of $m$ -gonal numbers

Universal mixed sums of generalized $4$ - and $8$ -gonal numbers