J. Champagne

works on

diophantine approximation 1 elementary methods 1 floor function 1 gcd 1 irrational sequences 1 probabilistic number theory 1

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math.NT2026

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

JÃ©rÃ©my Champagne

The paper determines the probability that the greatest common divisor of n and the integers ⌊α₁n⌋, ⌊α₂n²⌋, …, ⌊αₖnᵏ⌋ equals 1 for fixed irrational α_i, using an elementary approach…

math.NT2026

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

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. LÃª, 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 $I^\pm$ having the property that the sequence $(I^\pm p_{n})$ …

On the greatest common divisor of n,⌊I^±1​n⌋,⌊I^±2​n2⌋,...,⌊I^±k​nk⌋

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

Well-distribution modulo one and the primes

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