Jangwon Ju

activity

20182022

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

1 citations · 1 across the 5 of their papers we have counts for

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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.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…

Primitively universal quaternary quadratic forms

Tight universal octagonal forms

Tight universal sums of m-gonal numbers

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

Prime-universal diagonal quadratic forms

Ternary quadratic forms representing same integers

Tight universal sums of $m$ -gonal numbers