Olof Sisask

activity

20072023

most citedArithmetic progressions in sumsets and L^p-almost-periodicity

13 citations · 58 across the 12 of their papers we have counts for

collaborators

13 papers

math.NT2023★ 4 cited

An improvement to the Kelley-Meka bounds on three-term arithmetic progressions

Thomas F. Bloom, Olof Sisask

In a recent breakthrough Kelley and Meka proved a quasipolynomial upper bound for the density of sets of integers without non-trivial three-term arithmetic progressions. We present…

math.NT2023★ 8 cited

The Kelley--Meka bounds for sets free of three-term arithmetic progressions

Thomas F. Bloom, Olof Sisask

We give a self-contained exposition of the recent remarkable result of Kelley and Meka: if $A \subseteq {1, \dots, N}$ has no non-trivial three-term arithmetic progressions then $\…

math.NT2020★ 12 cited

Breaking the logarithmic barrier in Roth's theorem on arithmetic progressions

Thomas F. Bloom, Olof Sisask

We show that if $A \subset {1, \dots, N}$ contains no non-trivial three-term arithmetic progressions then $∣ A ∣ ≪ N / (lo g N)^{1 + c}$ for some absolute constant $c > 0$ . In…

math.CO2018★ 5 cited

Logarithmic bounds for Roth's theorem via almost-periodicity

Thomas F. Bloom, Olof Sisask

We give a new proof of logarithmic bounds for Roth's theorem on arithmetic progressions, namely that if $A \subset {1, 2, \dots, N}$ is free of three-term progressions, then $\lver…

math.CO2018★ 3 cited

Convolutions of sets with bounded VC-dimension are uniformly continuous

Olof Sisask

We study a notion of VC-dimension for subsets of groups, defining this for a set $A$ to be the VC-dimension of the family ${(x A) \cap A : x \in A \cdot A^{- 1}}$ . We show that if…

math.CO2014

Roth's theorem for four variables and additive structures in sums of sparse sets

Tomasz Schoen, Olof Sisask

We show that if a subset A of {1,...,N} does not contain any solutions to the equation x+y+z=3w with the variables not all equal, then A has size at most exp(-c(log N)^{1/7}) N, wh…