Waring's problem and Freiman's theorem

Abstract: Fre\u \i man proved that when $(k_i)$ is an increasing sequence of positive integers, then for each $j$, there exists $s=s(j)$ having the property that all large integers $n$ are represented as a sum of positive integral $k_i$-th powers (with $i\in \{j,j+1,\ldots ,s\}$) if and only if the series $1/k_1+1/k_2+\ldots $ diverges. We describe recent work joint with J\"org Br\"udern making Fre\u \i man's theorem effective. Some concrete examples will be described.

combinatoricsnumber theory

Audience: researchers in the topic

Combinatorial and additive number theory (CANY 2023)