Antal Balog

activity

20102016

most citedExpanders with superquadratic growth

3 citations · 5 across the 3 of their papers we have counts for

collaborators

3 papers

math.CO2016★ 3 cited

Expanders with superquadratic growth

Antal Balog, Oliver Roche-Newton, Dmitry Zhelezov

We will prove several expanders with exponent strictly greater than $2$ . For any finite set $A \subset R$ , we prove the following six-variable expander results: \begin{alig…

math.NT2014★ 2 cited

Sum of dilates in vector spaces

Antal Balog, George Shakan

Let $d \geq 2$ , $A \subset Z^{d}$ be finite and not contained in a translate of any hyperplane, and $q \in Z$ such that $∣ q ∣ > 1$ . We show $$|A+ q \cdot A| \geq (|q|…

math.NT2010

On the Number of Solutions of Exponential Congruences

Antal Balog, Kevin A. Broughan, Igor E. Shparlinski

For a prime $p$ and an integer $a \in Z$ we obtain nontrivial upper bounds on the number of solutions to the congruence $x^{x} \equiv a (mod p)$ , $1 \leq x \leq p - 1$ . We use these est…