Title：On infinite arithmetic progressions in sumsets

Abstract：Let $k$ be a positive integer. Denote by $D_{1/k}$ the least integer $d$ such that for every set $A$ of nonnegative integers with the lower density $1/k$, the set $(k+1)A$ contains an infinite arithmetic progression with difference at most $d$, where $(k+1)A$ is the set of all sums of $k+1$ elements (not necessarily distinct) of $A$. Confirming a conjecture of Chen and Li, we proved that $D_{1/k}=k^2+o(k^2)$. This is joint with Chen and Yang.

Speaker：Professor Lilu Zhao, Shandong University

Date：15:00pm-17:00pm 2023-5-12（Friday)

Venue: School of Mathematical Science Room 208

Organizer：School of Mathematical Science

Students and teachers who are interested in Number Theory are welcome.