Laurence P. Wijaya

activity

20242026

collaborators

5 papers

math.NT2026

Roth's Theorem in Super Smooth Numbers

Laurence P. Wijaya

We say that the set of $y$ -smooth numbers $S (N, y)$ up to $N$ is super smooth if $y = lo g^{K} N$ for a large fixed constant $K$ . We show that the Roth's theorem on arithmetic…

math.NT2026

Polynomial Corners Over finite Fields

Laurence P. Wijaya

Recently there has been some progress in understanding the density of a subset of $[N]^{2}$ that avoids polynomial patterns. Kravitz, Kuca, and Leng showed that if $P\in\mathbb{Z}[z]…

math.CO2025

On Monochromatic Solutions of Linear Equations Using At Least Three Colors

Laurence P. Wijaya

We study the number of monochromatic solution to linear equation in ${1, \dots, n}$ when we color the set by at least three colors. We consider the $r$ -commonness for $r \geq 3$ of…

math.NT2024

On Nonzero Coefficients of Binary Cyclotomic Polynomials

Igor E. Shparlinski, Laurence P. Wijaya

Let $ϑ (m)$ is number of nonzero coefficients in the $m$ -th cyclotomic polynomial. For real $I^^{3} > 0$ and $x \geq 2$ we define $$H_Î³(x)=\#\left\{m:~m=pq \le x, \ p<q\text{ pri…

math.NT2024

Sums of Kloosterman sums over square-free and smooth integers

Xuancheng Shao, Igor E. Shparlinski, Laurence P. Wijaya

Recently there has been a large number of works on bilinear sums with Kloosterman sums and on sums of Kloosterman sums twisted by arithmetic functions. Motivated by these, we consi…