Yu-chen Sun

activity

20222025

collaborators

4 papers

math.DS2025

Quantitative Convergence for Sparse Ergodic Averages in $L^{1}$

Ben Krause, Yu-Chen Sun

We provide a unified framework to proving pointwise convergence of sparse sequences, deterministic and random, at the $L^{1} (X)$ endpoint. Specifically, suppose that \[ a_n \in \{ \l…

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

The critical-window profile for $d_{k}$ in short intervals

Yu-Chen Sun

We establish an almost-all transition theorem for the $k$ -fold divisor function in short intervals. Let $k \geq 2$ be fixed, let $ℓ = lo g lo g X$ , and set \[ D_k(X)=(\log X)^{k\log…

math.NT2022

On the Balog-Ruzsa Theorem in short intervals

Yu-Chen Sun

In this paper we give a short interval version of the Balog-Ruzsa theorem concerning bounds for the $L_{1}$ norm of the exponential sum over $r$ -free numbers. As an application, we g…

Quantitative Convergence for Sparse Ergodic Averages in L1

Local divisor correlations in almost all short intervals

The critical-window profile for dk​ in short intervals

On the Balog-Ruzsa Theorem in short intervals

Quantitative Convergence for Sparse Ergodic Averages in $L^{1}$

The critical-window profile for $d_{k}$ in short intervals