J. Champagne

activity

20192026

collaborators

5 papers

math.NT2026

On the greatest common divisor of $n, ⌊ α_{1} n ⌋, ⌊ α_{2} n^{2} ⌋, ..., ⌊ α_{k} n^{k} ⌋$

Jérémy Champagne

We answer a question of Bergelson and Richter about the probability of the relation $g cd (n, ⌊ α_{1} n ⌋, ⌊ α_{2} n^{2} ⌋, ..., ⌊ α_{k} n^{k} ⌋) = 1$ for $n\in\mathbb{N}…

math.NT2025

Equidistribution of polynomial sequences in function fields: resolution of a conjecture

Jérémy Champagne, Zhenchao Ge, Thái Hoàng Lê +2

Let $F_{q}$ be the finite field of $q$ elements having characteristic $p$ , and denote by $K_{\infty} = F_{q} ((1/ t))$ the field of formal Laurent series in $1/ t$ . We…

math.NT2024

Well-distribution modulo one and the primes

J. Champagne, T. H. Lê, Y. -R. Liu +1

Let $(p_{n})$ denote the sequence of prime numbers, with $2 = p_{1} < p_{2} < \dots$ . We demonstrate the existence of an irrational number $α$ having the property that the sequence $(α p_{n})$ i…

math.NT2022

Diophantine approximation with constraints

Jérémy Champagne, Damien Roy

Following Schmidt, Thurnheer and Bugeaud-Kristensen, we study how Dirichlet's theorem on linear forms needs to be modified when one requires that the vectors of coefficients of the…

math.NT2019

A transference inequality for rational approximation to points in geometric progression