Expanders with Superquadratic Growth
Keywords:
Sum-product estimates, Expanders, Discrete geometry
Abstract
We prove several expanders with exponent strictly greater than 2. For any finite set A⊂R, we prove the following six-variable expander results:
|(A−A)(A−A)(A−A)|≫|A|2+18log1716|A|,
|A+AA+A+AA|≫|A|2+217log1617|A|,
|AA+AAA+A|≫|A|2+18log|A|,
|AA+AAA+A|≫|A|2+18log|A|.