T. Schoen

activity

20072023

most citedAdditive dimension and a theorem of Sanders

13 citations · 26 across the 12 of their papers we have counts for

collaborators

Showing 2023Show all

3 papers · 1 filter

math.CO2023

New bounds in the Bogolyubov-Ruzsa lemma

Tomasz Kosciuszko, Tomasz Schoen

We establish new bounds in the Bogolyubov-Ruzsa lemma, demonstrating that if A is a subset of a finite abelian group with density alpha, then 3A-3A contains a Bohr set of rank O(lo…

math.CO2023

On convex equations

Tomasz Schoen

We prove that every subset of ${1, \dots, N}$ which does not contain any solutions to the equation $x + y + z = 3 w$ has at most $exp (- c (lo g N)^{1/5 + o (1)}) N$ elements, for some $c > 0$ .…

math.CO2023

Note on the Theorem of Balog, Szemerédi, and Gowers

Christian Reiher, Tomasz Schoen

We prove that every additive set $A$ with energy $E (A) \geq ∣ A ∣^{3} / K$ has a subset $A^{'} \subseteq A$ of size $∣ A^{'} ∣ \geq (1 - ε) K^{- 1/2} ∣ A ∣$ such that $|A'-A'|\le O_\varepsilon(K^{…