I. Shkredov

activity

20042026

most citedSome new inequalities in additive combinatorics

58 citations · 373 across the 79 of their papers we have counts for

collaborators

Showing 2022Show all

5 papers · 1 filter

math.NT2022

On Korobov bound concerning Zaremba's conjecture

Nikolay Moshchevitin, Brendan Murphy, Ilya Shkredov

We prove in particular that for any sufficiently large prime $p$ there is $1 \leq a < p$ such that all partial quotients of $a / p$ are bounded by $O (lo g p / lo g lo g p)$ . For composite…

math.NT2022

The popularity gap

Vsevolod F. Lev, Ilya D. Shkredov

Suppose that $A$ is a finite, nonempty subset of a cyclic group of either infinite or prime order. We show that if the difference set $A - A$ is ``not too large'', then there is a no…

math.CO2022

Additive dimension and the growth of sets

Ilya D. Shkredov

We develop the theory of the additive dimension $dim (A)$ , i.e. the size of a maximal dissociated subset of a set $A$ . It was shown that the additive dimension is closely con…

math.NT2022

On the random Chowla conjecture

Oleksiy Klurman, Ilya D. Shkredov, Max Wenqiang Xu

We show that for a Steinhaus random multiplicative function $f : N \to D$ and any polynomial $P (x) \in Z [x]$ of $deg P \geq 2$ which is not of the form $…

math.NT2022

On a paucity result in Incidence Geometry

Ilya D. Shkredov

We obtain some asymptotic formulae (with power savings in their error terms) for the number of quadruples in the Cartesian product of an arbitrary set $A \subset R$ and fo…