58 citations · 373 across the 79 of their papers we have counts for
5 papers · 2 filters
On multiplicative properties of combinatorial cubes
Ilya D. Shkredov
We obtain a series of lower bounds for the product set of combinatorial cubes, as well as some non--trivial upper estimates for the multiplicative energy of such sets.
The Uniformity Conjecture in Additive Combinatorics
Ilya D. Shkredov, Jozsef Solymosi
In this paper we show examples for applications of the Bombieri-Lang conjecture in additive combinatorics, giving bounds on the cardinality of sumsets of squares and higher powers…
On the spectral gap and the diameter of Cayley graphs
Ilya D. Shkredov
We obtain a new bound connecting the first non--trivial eigenvalue of the Laplace operator of a graph and the diameter of the graph, which is effective for graphs with small diamet…
--functions and sum--free sets
Tomasz Schoen, Ilya D. Shkredov
For set define by the size of the largest sum--free subset of Alon and Kleitman showed that ${\mathsf{sf}} (A) \ge |A|/3+O(|A|/…
Bounds of Trilinear and Trinomial Exponential Sums
Simon Macourt, Giorgis Petridis, Ilya D. Shkredov +1
We prove, for a sufficiently small subset of a prime residue field, an estimate on the number of solutions to the equation w…