4 papers
math.DS2025
Quantitative Convergence for Sparse Ergodic Averages in
Ben Krause, Yu-Chen Sun
We provide a unified framework to proving pointwise convergence of sparse sequences, deterministic and random, at the 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 be natural numbers, and let denote the -fold and -fold divisor functions, respectively. We analyse the asymptotic behavior of the sum $\sum_{x<n\l…
math.NT2024
The critical-window profile for in short intervals
Yu-Chen Sun
We establish an almost-all transition theorem for the -fold divisor function in short intervals. Let be fixed, let , 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 norm of the exponential sum over -free numbers. As an application, we g…