arXiv subjects

Néo Tardy

Publications and source records attributed to Néo Tardy.

3 recordsLinked to original sources

arXiv2026

Two-point correlations of multiplicative functions with dense orbits

Let $f,g:\mathbb{N}\to\mathbb{T}$ be completely multiplicative functions with dense images in the complex unit circle $\mathbb{T}$. We prove that, for every non-empty open set $U \subset \mathbb{T}^2$, the set of integers $n$ such that $(f(n),g(n+1)) \in U$ has positive lower logarithmic density, unless the pair $(f,g)$ is of a special form. This result strengthens earlier theorems of Klurman and Mangerel, as well as of Charamaras, Mountakis, and Tsinas, and yields substantially simpler proofs.

math.NT↗

arXiv2026

Integers divisible by a shifted prime in a given interval

In this paper we study the behaviour of $H^*(x,y,z)$, the number of integers less than $x$ possessing a divisor in the interval $(y,z]$ of the form $p-1$, where $p$ is a prime, for all values of $y = y(x)$ and $z= z(y)$. We observe multiple phase transitions at critical values of $z$ in terms of $x$ and $y$ guided largely by the anatomy of $n$. Our results generalize a result of Ford from 2017, which corresponds to the case $z = x$.

math.NT↗

arXiv2026

Large values of shifted mixed character sums

We consider sums of the form $$F_χ(α,β;θ) := \sum_{αp<n\leβp}χ(n)e(nθ),$$ where $χ$ is a non-principal Dirichlet character modulo a prime number $p$. We prove that $$ \sqrt p \log \log p \ll \max_{0 \le θ< 1}{\left|F_χ(α,β;θ)\right|} \ll \sqrt{p}\log p, $$ generalizing an old result of Montgomery as well as a recent result of Iggidr in two aspects: we allow general non-principal characters $χ$, and we consider incomplete mixed character sums.

math.NT↗