Pairwise coprime integers in short sequences with polynomial growth
Speaker:
Jean-Marc Deshouillers, Institut de Mathématiques de Bordeaux
Date and Time:
Tuesday, May 28, 2024 - 9:55am to 10:30am
Location:
Fields Institute, Room 230
Abstract:
In 2023, M. Drmota, C. M\"{u}llner and I showed that for $c$ in $(1,2)$ and $H$ in $\mathbb{N}$, the set $\mathcal{N}(c,H)$ consisting of the integers $n$ such that all the numbers
$\lfloor (n+1)^c\rfloor, \lfloor (n+2)^c\rfloor, \cdots, \lfloor (n+H)^c\rfloor \, \text{ are pairwise coprime,}$
is infinite. I'll present parts of a joint work in progress with H. Iwaniec, which implies that for any $c$ and $H$ as above, the set $\mathcal{N}(c,H)$ has a positive asymptotic density.
