13 citations · 58 across the 12 of their papers we have counts for
7 papers · 1 filter
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 is free of three-term progressions, then $\lver…
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 to be the VC-dimension of the family . We show that if…
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…
Convergence results for systems of linear forms on cyclic groups, and periodic nilsequences
Pablo Candela, Olof Sisask
Given a positive integer and real number , let denote the minimum, over all sets of size at least , of the normalize…
A removal lemma for linear configurations in subsets of the circle
Pablo Candela, Olof Sisask
We obtain a removal lemma for systems of linear equations over the circle group, using a similar result for finite fields due to Král, Serra and Vena, and we discuss some applicati…
On the asymptotic maximal density of a set avoiding solutions to linear equations modulo a prime
Pablo Candela, Olof Sisask
Given a finite family F of linear forms with integer coefficients, and a compact abelian group G, an F-free set in G is a measurable set which does not contain solutions to any equ…