W. Wongcharoenbhorn

activity

20222025

collaborators

4 papers

math.NT2025

Variance of square-full integers in short intervals and arithmetic progressions

Yotsanan Meemark, Watcharakiete Wongcharoenbhorn

Define a natural number $n$ as a \textit{square-full} integer if for every prime $p$ such that $p ∣ n$ , we have $p^{2} ∣ n$ . In this paper, we establish an upper bound on the variance of…

math.NT2024

An average number of square-free values of polynomials

Watcharakiete Wongcharoenbhorn, Yotsanan Meemark

The well-known result states that the square-free counting function up to $N$ is $N / ζ (2) + O (N^{1/2})$ . This corresponds to the identity polynomial $Id (x)$ . It is expected tha…

math.NT2024

Square-full values of quadratic polynomials

Watcharakiete Wongcharoenbhorn, Yotsanan Meemark

A $square-full$ number is a positive integer for which all its prime divisors divide itself at least twice. The counting function of square-full integers of the form $f(n)…

math.NT2022

Three consecutive near-square squarefree numbers

W. Wongcharoenbhorn

In this note, we prove by using T. Estermann's and S. Dimitrov's arguments with an elementary inequality that there are infinitely many $n$ for which all of the numbers $n^2+1,n^2+…