58 citations · 373 across the 79 of their papers we have counts for
108 papers
Energy Estimation of the Hamming Slice and its Applications
Aniruddha Biswas, Jihun Hwang, Hemanta K. Maji +2
Let , where , and let be the residues whose canonical -digit binary expansion has Hamming weight . We obtain, in par…
On some results of Korobov and Larcher and Zaremba's conjecture
Ilya D. Shkredov
We prove, in particular, the well--known Zaremba conjecture from the theory of continued fractions for any prime denominator. More precisely, we show, firstly, that under some mild…
Structure theory of set addition with two operations
Aliaksei Semchankau, Ilya Shkredov
We take the first step toward a structure theory that includes both operations of a ring . More precisely, we prove a series of inverse results for the structure of se…
On common energies and sumsets II
Ilya D. Shkredov
We continue to study the relationship between the size of the sum of a set and the common energy of its subsets. We find a rather sharp subexponential dependence between the doubli…
On Fourier coefficients of sets with small doubling
Ilya D. Shkredov
Let be a subset of a finite abelian group such that has a small difference set and the density of is small. We prove that, counter--intuitively, the smallness (in…
On common energies and sumsets
Ilya D. Shkredov
We obtain a polynomial criterion for a set to have a small doubling in terms of the common energy of its subsets.