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pro vyhledávání: '"Semchankau, Aliaksei"'
The paper deals with a problem of Additive Combinatorics. Let ${\mathbf G}$ be a finite abelian group of order $N$. We prove that the number of subset triples $A,B,C\subset {\mathbf G}$ such that for any $x\in A$, $y\in B$ and $z\in C$ one has $x+y\n
Externí odkaz:
http://arxiv.org/abs/2012.13433
Autor:
Semchankau, Aliaksei
For $p$ being a large prime number, and $A \subset \mathbb{F}_p$ we prove the following: $(i)$ If $A(A+A)$ does not cover all nonzero residues in $\mathbb{F}_p$, then $|A| < p/8 + o(p)$. $(ii)$ If $A$ is both sum-free and satisfies $A = A^*$, then $|
Externí odkaz:
http://arxiv.org/abs/2011.11468
Autor:
Semchankau, Aliaksei
Publikováno v:
In Journal of Number Theory August 2024
Autor:
Semchankau, Aliaksei
Publikováno v:
Math Notes 102, 396-402 (2017)
We consider the problem of determining the maximum cardinality of a subset containing no arithmetic progressions of length $k$ in a given set of size $n$. It is proved that it is sufficient, in a certain sense, to consider the interval $[1,\dots, n]$
Externí odkaz:
http://arxiv.org/abs/2010.04490
Given a subset of real numbers $A$ with small product $AA$ we obtain a new upper bound for the additive energy of $A$. The proof uses a natural observation that level sets of convolutions of the characteristic function of $A$ have small product with
Externí odkaz:
http://arxiv.org/abs/1911.12005
Autor:
Semchankau, Aliaksei
We will study the solutions to the equation $f(n) - g(n) = c$, where $f$ and $g$ are multiplicative functions and $c$ is a constant. More precisely, we prove that the number of solutions does not exceed $c^{1-\epsilon}$ when $f, g$ and solutions $n$
Externí odkaz:
http://arxiv.org/abs/1901.01846
Publikováno v:
In European Journal of Combinatorics February 2022 100
Akademický článek
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Publikováno v:
Revista Mathematica Iberoamericana; 2024, Vol. 40 Issue 2, p637-648, 12p
Autor:
Semchankau, Aliaksei
We will study the solutions to the equation $f(n) - g(n) = c$, where $f$ and $g$ are multiplicative functions and $c$ is a constant. More precisely, we prove that the number of solutions does not exceed $c^{1-��}$ when $f, g$ and solutions $n$ sa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0d32306ecf3d662feec4d8531547ce5f