New York Number Theory Seminar
March 06, 2003, 3:30 PM in Room 5417
- Speaker:
- Jozsef Solymosi (University of California, San Diego)
- Title:
- On sums and products of complex numbers
- Abstract:
- Improving earlier results of M.Nathanson and Gy.Elekes, we prove
the following bound on sumsets. If $A$ is a finite set of
complex numbers, then $$c|A|^{14}<\log^3{|A|}|A+A|^8|AA|^3,$$
whence it's impossible that both $|A+A|$ and $|AA|$ are much
smaller than $|A|^{14/11}$.