Dayoon Park

activity

20192021

m

-gonal forms

1 citations · 2 across the 10 of their papers we have counts for

collaborators

10 papers

math.NT2021

Representation of $m$ -gonal forms over $N_{0}$ and a finiteness theorem for universal original version's $m$ -gonal forms

Dayoon Park

In this article, we consider the representation of $m$ -gonal forms over $N_{0}$ . We show that any $m$ -gonal forms over $N_{0}$ of rank $\geq 5$ is almost regular and pon…

math.NT2021

Non-almost regular quaternary $m$ -gonal forms

Dayoon Park

The maximal $n$ which admits a non-almost regular $m$ -gonal form of rank $n$ is $4$ . In this article, we consider the $m$ -gonal forms of rank $4$ which is not almost regular.

math.NT2021

Representations of almost regular m-gonal forms II

Dayoon Park

It is known that any $m$ -gonal form of rank $n \geq 5$ is almost regular. On the other words, any $m$ -gonal form of rank $n \geq 5$ represents every sufficiently large integer which…

math.NT2021

Representations of almost regular m-gonal forms I

Dayoon Park

It is known that any $m$ -gonal form of $\rank n \ge 5$ is almost regular. In this article, we study the sufficiently large integers which are represented by (almost regular) $m$ -go…

math.NT2021

Completing an universal $m$ -gonal form with a closing unary piece

Dayoon Park

In this paper, we show that for any $m$ -gonal form $F_{m} (x)$ with $m \geq 12$ which represents every positive integer up to $m - 4$ , by putting together only unary $m$ -gonal fo…

math.NT2021

Determining universality of $m$ -gonal form with first five coefficients

Dayoon Park

In this paper, we classify the $(a_{1}, a_{2}, a_{3}, a_{4}, a_{5})$ for which the universality of an $m$ -gonal form $F_{m} (x)$ having its first five coefficients as $(a_1,a_2,a_3,a_4,a_5)…

math.NT2020

The rank of universal $m$ -gonal forms

Byeong Moon Kim, Dayoon Park

In this article, we consider the rank of universal $m$ -gonal forms for all sufficiently large $m$ . Especially, we determine the minimal rank of universal $m$ -gonal form and the max…

math.NT2020★ 1 cited

A finiteness theorem for universal $m$ -gonal forms

Byeong Moon Kim, Dayoon Park

In this paper, we study the set of positive integers that characterize the universality of $m$ -gonal form.

math.NT2020★ 1 cited

Regular $m$ -gonal forms

Byeong Moon Kim, Dayoon Park

In this paper, we show that for a fixed rank $n$ , there are only finitely many $m$ for which there is a regular $m$ -gonal form of rank $n$ and determine every type of the (generali…

math.NT2019

Fermat's polygonal number theorem for repeated generalized polygonal numbers

Soumyarup Banerjee, Manav Batavia, Ben Kane +5

In this paper, we consider sums of generalized polygonal numbers with repeats, generalizing Fermat's polygonal number theorem which was proven by Cauchy. In particular, we obtain t…

Representation of m-gonal forms over N0​ and a finiteness theorem for universal original version's m-gonal forms

Non-almost regular quaternary m-gonal forms

Representations of almost regular m-gonal forms II

Representations of almost regular m-gonal forms I

Completing an universal m-gonal form with a closing unary piece

Determining universality of m-gonal form with first five coefficients

The rank of universal m-gonal forms

A finiteness theorem for universal m-gonal forms

Regular m-gonal forms

Fermat's polygonal number theorem for repeated generalized polygonal numbers

Representation of $m$ -gonal forms over $N_{0}$ and a finiteness theorem for universal original version's $m$ -gonal forms

Non-almost regular quaternary $m$ -gonal forms

Completing an universal $m$ -gonal form with a closing unary piece

Determining universality of $m$ -gonal form with first five coefficients

The rank of universal $m$ -gonal forms

A finiteness theorem for universal $m$ -gonal forms

Regular $m$ -gonal forms