- Series
- Combinatorics Seminar
- Time
- Friday, January 22, 2016 - 4:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 154
- Speaker
- Georgios Petridis – University of Rochester – g.petridis@rochester.edu
- Organizer
- Esther Ezra
We show that there exists an absolute constant c>0 with the following property. Let A be a set in a finite field with q elements. If |A|>q^{2/3-c}, then the set (A-A)(A-A) consisting of products of pairwise differences of elements of A contains at least q/2 elements. It appears that this is the first instance in the literature where such a conclusion is reached for such type sum-product-in-finite-fileds questions for sets of smaller cardinality than q^{2/3}. Similar questions have been investigated by Hart-Iosevich-Solymosi and Balog.