Zobrazeno 1 - 10
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pro vyhledávání: '"Ju, Jangwon"'
Autor:
Ju, Jangwon
For an arbitrary integer $x$, an integer of the form $T(x)\!=\!\frac{x^2+x}{2}$ is called a triangular number. Let $\alpha_1,\dots,\alpha_k$ be positive integers. A sum $\Delta_{\alpha_1,\dots,\alpha_k}(x_1,\dots,x_k)=\alpha_1 T(x_1)+\cdots+\alpha_k
Externí odkaz:
http://arxiv.org/abs/2408.11310
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 $f$, but not $f$ itself. It was proved that the minimal rank of isola
Externí odkaz:
http://arxiv.org/abs/2308.04720
A (positive definite and integral) quadratic form $f$ is said to be $\textit{universal}$ if it represents all positive integers, and is said to be $\textit{primitively universal}$ if it represents all positive integers primitively. We also say $f$ is
Externí odkaz:
http://arxiv.org/abs/2202.13573
Autor:
Ju, Jangwon, Kim, Mingyu
Let $P_8(x)=3x^2-2x$. For positive integers $a_1,a_2,\dots,a_k$, a polynomial of the form $a_1P_8(x_1)+a_2P_8(x_2)+\cdots+a_kP_8(x_k)$ is called an octagonal form. For a positive integer $n$, an octagonal form is called tight $\mathcal T(n)$-universa
Externí odkaz:
http://arxiv.org/abs/2202.09304
Autor:
Ju, Jangwon, Kim, Mingyu
For a positive integer $n$, the set of all integers greater than or equal to $n$ is denoted by $\mathcal T(n)$. A sum of generalized $m$-gonal numbers $g$ is called tight $\mathcal T(n)$-universal if the set of all nonzero integers represented by $g$
Externí odkaz:
http://arxiv.org/abs/2202.09296
Autor:
Ju, Jangwon
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 $\alpha_1,\alpha_2,\dots,\alpha_k$, a sum $\Delta_{\alpha_1,\alpha_2,\dots,\alpha_k}(x_1,x_2,\dots,x_k)=\alpha_1 T(x_1)+\
Externí odkaz:
http://arxiv.org/abs/2201.04355
Autor:
Ju, Jangwon, Kim, Daejun
In this article, we study the representability of integers as sums of pentagonal numbers, where a pentagonal number is an integer of the form $P_5(x)=\frac{3x^2-x}{2}$ for some non-negative integer $x$. In particular, we prove the "pentagonal theorem
Externí odkaz:
http://arxiv.org/abs/2010.16123
A (positive definite and integral) quadratic form is said to be $\textit{prime-universal}$ if it represents all primes. Recently, Doyle and Williams in [2] classified all prime-universal diagonal ternary quadratic forms, and all prime-universal diago
Externí odkaz:
http://arxiv.org/abs/2006.14786
Autor:
Ju, Jangwon
In 1997, Kaplansky conjectured that if two positive definite ternary quadratic forms with integer coefficients have perfectly identical integral representations, then they are isometric, both regular, or included either of two families of ternary qua
Externí odkaz:
http://arxiv.org/abs/2002.02205
Publikováno v:
In Journal of Number Theory January 2023 242:181-207
