Number Theory Seminar

Tuesday, March 21, 2023 10:00 am - 10:00 am EDT (GMT -04:00)

Note: The time of this talk is different from the usual Number Theory Seminar time.

Trevor Wooley, Purdue University

"Waring's problem and Freiman's theorem"

Freiman 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 $i\in \{ j,j + 1,...,s\}$) if and only if $1/k_1 + 1/k_2 + · · ·$ diverges. We describe recent work joint with Joerg Bruedern making Freiman's theorem effective. Some concrete examples will be described, as well as the underlying progress on Waring's problem.

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