4 papers · 1 filter
Van der Waerden's theorem on arithmetic progressions -- a survey of some historical and modern developments
Vitaly Bergelson, Florian K. Richter
Van der Waerden's theorem, published in Nieuw. Arch. Wisk. 15 (1927), acted as a catalyst for major further developments in Ramsey theory. In this survey, we delve into the legacy…
Polynomial actions of rings of integers of global fields and quasirandomness of Paley-type graphs
Ethan Ackelsberg, Vitaly Bergelson
The goal of this paper is to undertake an in-depth study of the phenomenon behind the Furstenberg--Sárközy theorem, which, in its modern form due to Kamae and Mendès-France, sta…
On the Polynomial Szemerédi Theorem in Finite Commutative Rings
Vitaly Bergelson, Andrew Best
The polynomial Szemerédi theorem implies that, for any , any family of nonconstant polynomials with constant term zero, an…
On the interplay between notions of additive and multiplicative largeness and its combinatorial applications
Vitaly Bergelson, Daniel Glasscock
Many natural notions of additive and multiplicative largeness arise from results in Ramsey theory. In this paper, we explain the relationships between these notions for subsets of…