N. Tardy

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math.NT2026

Integers divisible by a shifted prime in a given interval

Rebecca Abi Abdallah, Valeriya Kovaleva, Jeremy Schlitt +1

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…

math.NT2026

Two-point correlations of multiplicative functions with dense orbits

Néo Tardy

Let $f, g : N \to T$ be completely multiplicative functions with dense images in the complex unit circle $T$ . We prove that, for every non-empty open set $U \…

math.NT2026

Large values of shifted mixed character sums

Néo Tardy

We consider sums of the form $F_{χ} (α, β; θ) := α p < n \leq β p \sum χ (n) e (n θ),$ where $χ$ is a non-principal Dirichlet character modulo a prime number $p$ . We prove that $$ \sqrt p \log…