46 citations · 279 across the 57 of their papers we have counts for
10 papers · 1 filter
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, states…
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, and…
Discordant sets and ergodic Ramsey theory
Vitaly Bergelson, Jake Huryn, Rushil Raghavan
We explore the properties of non-piecewise syndetic sets with positive upper density, which we call "discordant", in countably infinite amenable (semi)groups. Sets of this kind are…
Iterated differences sets, diophantine approximations and applications
Vitaly Bergelson, Rigoberto Zelada
Let be an odd real polynomial (i.e. a polynomial of the form ). We utilize sets of iterated differences to establish new results about sets of the…
Multiplicative richness of additively large sets in
Vitaly Bergelson, Daniel Glasscock
In their proof of the IP Szemerédi theorem, a far reaching extension of the classic theorem of Szemerédi on arithmetic progressions, Furstenberg and Katznelson introduced an import…
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…