Mengdi Wang

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math.NT2025

Local divisor correlations in almost all short intervals

Javier Pliego, Yu-Chen Sun, Mengdi Wang

Let $k, l \geq 2$ be natural numbers, and let $d_{k}, d_{l}$ denote the $k$ -fold and $l$ -fold divisor functions, respectively. We analyse the asymptotic behavior of the sum $\sum_{x<n\l…

math.NT2024

Local Fourier uniformity of higher divisor functions on average

Mengdi Wang

Let $I ¨ _{k}$ be the $k$ -fold divisor function. By constructing an approximant of $I ¨ _{k}$ , denoted as $I ¨ _{k}^{*}$ , which is a normalized truncation of the $k$ -fold divisor function, we pr…