Mingyu Kim

activity

20182022

most citedThe number of representations by a ternary sum of triangular numbers

2 citations · 2 across the 11 of their papers we have counts for

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11 papers · 1 filter

math.NT2022

Regular triangular forms of rank exceeding 3

Mingyu Kim

A triangular form is defined to be an integer-valued quadratic polynomial of the form $a_{1} P_{3} (x_{1}) + a_{2} P_{3} (x_{2}) + \dots + a_{k} P_{3} (x_{k})$ where $a_{i}^{'} s$ are positive integers and $P_3(x)=x…

math.NT2022

A classification of regular diagonal quadratic forms

Mingyu Kim

A positive-definite integral quadratic form is called regular if it represents every positive integer which is locally represented. In this article, we classify all regular diagona…

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.NT2021

Tight universal triangular forms

Mingyu Kim

For a subset $S$ of nonnegative integers and a vector $a = (a_{1}, \dots, a_{k})$ of positive integers, let $V_{S}^{'} (a) = {a_{1} s_{1} + \dots + a_{k} s_{k} : s_{i} \in S} ∖ {0}$ …

Regular triangular forms of rank exceeding 3

A classification of regular diagonal quadratic forms

Primitively universal quaternary quadratic forms

Tight universal octagonal forms

Tight universal sums of m-gonal numbers

Tight universal triangular forms

Tight universal sums of $m$ -gonal numbers