Student Number Theory seminar

Shuntaro Yamagishi, Pure Mathematics, University of Waterloo

"Sidon Problem in polynomial ring over finite field"

Given a sequence of natural numbers $\omega$, we define $r_n(\omega) = | \{ (a,b) : a+b = n, a< b, \text{ and } a,b \in \omega  \}|$.  In 1954, Erdos proved that there exists a sequence $\omega$ such that $\log n \ll r_n(\omega) \ll \log n$. We consider the analogue of this question in polynomial ring over finite field.