13 citations · 32 across the 10 of their papers we have counts for
13 papers
The sum-product conjecture is false for real numbers
Thomas F Bloom, Will Sawin, Carl Schildkraut +1
We disprove the sum-product conjecture for real numbers by constructing arbitrarily large (whose elements are algebraic integers in a number field of degree $…
Convexity, Elementary Methods, and Distances
Oliver Roche-Newton, Dmitrii Zhelezov
This paper considers an extremal version of the Erdős distinct distances problem. For a point set , let denote the set of all Euclidean distances dete…
The sum-product problem for integers with few prime factors
Brandon Hanson, Misha Rudnev, Ilya Shkredov +1
It was asked by E. Szemerédi if, for a finite set , one can improve estimates for , under the constraint that all integers involved ha…
A Weighted Prékopa-Leindler inequality and sumsets with quasicubes
Ben Green, Dávid Matolcsi, Imre Ruzsa +2
We give a short, self-contained proof of two key results from a paper of four of the authors. The first is a kind of weighted discrete Prékopa-Leindler inequality. This is then app…
An analytic approach to cardinalities of sumsets
Dávid Matolcsi, Imre Ruzsa, George Shakan +1
Let be a positive integer and finite. We study $$β(U) : = \inf_{\substack{A , B \neq \emptyset \\ \text{finite}}} \frac{|A+B+U|}{|A|^{1/2}{|B|^{1/2}}},…
Query complexity and the polynomial Freiman-Ruzsa conjecture
Dmitrii Zhelezov, Dömötör Pálvölgyi
We prove a query complexity variant of the weak polynomial Freiman-Ruzsa conjecture in the following form. For any , a set with doubling has a su…
On iterated product sets with shifts II
Brandon Hanson, Oliver Roche-Newton, Dmitrii Zhelezov
The main result of this paper is the following: for all there exists such that \[ \max \{ |A^{(k)}|, |(A+u)^{(k)}| \} \geq |A|^b, \] for any finite $A \s…
On iterated product sets with shifts
Brandon Hanson, Oliver Roche-Newton, Dmitrii Zhelezov
We prove that, for any finite set with and any positive integer , the -fold product set of the shift satisfies the bound $$| \{(a…
Bourgain-Chang's proof of the weak Erdős-Szemerédi conjecture
Dmitrii Zhelezov
This is an exposition of the following `weak' Erdős-Szemerédi conjecture for integer sets proved by Bourgain and Chang in 2004. For any there exists such that for…
Convex sequences may have thin additive bases
Imre Z. Ruzsa, Dmitrii Zhelezov
For a fixed we construct an arbitrarily large set of size such that its sum set contains a convex sequence of size , answering a question of Hegarty.
On additive bases of sets with small product set
Ilya D. Shkredov, Dmitrii Zhelezov
We prove that finite sets of real numbers satisfying with sufficiently small cannot have small additive bases nor can they be written as a set of sums…
Discrete spheres and arithmetic progressions in product sets
Dmitrii Zhelezov
We prove that if is a set of positive integers such that contains an arithmetic progression of length , then for some absolute , $$ π(M) + C \frac {M^{…
On additive shifts of multiplicative almost-subgroups in finite fields
Dmitrii Zhelezov
We prove that for sets with and a fixed holds In…