We prove several expanders with exponent strictly greater than $2$. For any finite set $A \subset \mathbb R$, we prove the following six-variable expander results:$|(A-A)(A-A)(A-A)| \gg \frac{|A|^{2+\frac{1}{8}}}{\log^{\frac{17}{16}}|A|},$$\left|\frac{A+A}{A+A}+\frac{A}{A}\right| \gg \frac{|A|^{2+\frac{2}{17}}}{\log^{\frac{16}{17}}|A|},$$\left|\frac{AA+AA}{A+A}\right| \gg \frac{|A|^{2+\frac{1}{8}}}{\log |A|},$$\left|\frac{AA+A}{AA+A}\right| \gg \frac{|A|^{2+\frac{1}{8}}}{\log |A|}.$
@article{10_37236_7050,
author = {Antal Balog and Oliver Roche-Newton and Dmitry Zhelezov},
title = {Expanders with superquadratic growth},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {3},
doi = {10.37236/7050},
zbl = {1373.52021},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7050/}
}
TY - JOUR
AU - Antal Balog
AU - Oliver Roche-Newton
AU - Dmitry Zhelezov
TI - Expanders with superquadratic growth
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/7050/
DO - 10.37236/7050
ID - 10_37236_7050
ER -
%0 Journal Article
%A Antal Balog
%A Oliver Roche-Newton
%A Dmitry Zhelezov
%T Expanders with superquadratic growth
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/7050/
%R 10.37236/7050
%F 10_37236_7050
Antal Balog; Oliver Roche-Newton; Dmitry Zhelezov. Expanders with superquadratic growth. The electronic journal of combinatorics, Tome 24 (2017) no. 3. doi: 10.37236/7050
