Javier Pliego

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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

On Vu's theorem in Waring's problem for thinner sequences

Javier Pliego

Let $k \in N$ and $s \geq k (lo g k + 3.20032)$ . Let $N_{0}^{k}$ be the set of $k$ -th powers of nonnegative integers. Assume that $ψ$ is an increasing function tending…

math.NT2024

On the Erdős-Turán Conjecture and the growth of $B_{2} [g]$ sequences

Javier Pliego

When $g \in N$ we say that $A \subset N$ is a $B_{2} [g]$ sequence if every $m \in N$ has at most $g$ distinct representations of the shape $m = b_{1} + b_{2}$ with…

Local divisor correlations in almost all short intervals

On Vu's theorem in Waring's problem for thinner sequences

On the Erdős-Turán Conjecture and the growth of B2​[g] sequences

On the Erdős-Turán Conjecture and the growth of $B_{2} [g]$ sequences