A. Balog

activity

20072019

most citedThe prime geodesic theorem in square mean

14 citations · 31 across the 8 of their papers we have counts for

collaborators

11 papers

math.NT2019

Bykovskii-type theorem for the Picard manifold

Antal Balog, András Biró, Giacomo Cherubini +1

We generalise a result of Bykovskii to the Gaussian integers and prove an asymptotic formula for the prime geodesic theorem in short intervals on the Picard manifold. Previous work…

math.NT2018★ 14 cited

The prime geodesic theorem in square mean

Antal Balog, András Biró, Gergely Harcos +1

We strengthen the recent result of Cherubini and Guerreiro on the square mean of the error term in the prime geodesic theorem for $PSL_{2} (Z)$ . We also develop a sh…

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.NT2015★ 4 cited

A low-energy decomposition theorem

Antal Balog, Trevor D. Wooley

We prove that any finite set of real numbers can be split into two parts, one part being highly non-additive and the other highly non-multiplicative.

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.NT2014

Gaps between fractional parts, and additive combinatorics

Antal Balog, Andrew Granville, Jozsef Solymosi

We give bounds on the number of distinct differences $N_{a} - a$ as $a$ varies over all elements of a given finite set $A$ , and $N_{a}$ is a nearest neighbour to $a$ .