arXiv subjects

Alexey Glibichuk

Publications and source records attributed to Alexey Glibichuk.

2 recordsLinked to original sources

arXiv2011

Average estimate for additive energy in prime field

Assume that $A\subseteq \Fp, B\subseteq \Fp^{*}$, $\1/4\leqslant\frac{|B|}{|A|},$ $|A|=p^α, |B|=p^β$. We will prove that for $p\geqslant p_0(β)$ one has $$\sum_{b\in B}E_{+}(A, bA)\leqslant 15 p^{-\frac{\min\{β, 1-α\}}{308}}|A|^3|B|.$$ Here $E_{+}(A, bA)$ is an additive energy between subset $A$ and it's multiplicative shift $bA$. This improves previously known estimates of this type.

math.NT↗

arXiv2008

Additive properties of product sets in an arbitrary finite field

It is proved that for any two subsets $A$ and $B$ of an arbitrary finite field $\Fq$ such that $|A||B|>q$ the identity $16AB=\Fq$ holds. Moreover, it is established that for every subsets $X, Y\subset \Fq$ with the property $|X||Y|\geqslant 2q$ the equality $8XY=\Fq$ holds.

math.NT↗