Number Theory Seminar

Dimitris Koukoulopoulos, Université de Montréal

"On the Duffin-Schaeffer conjecture"

Let $S$ be a sequence of integers. We wish to understand how well we can approximate a "typical'' real number using reduced fractions whose denominators lie in $S$. To this end, we associate to each $q\in S$ an acceptable error $\Delta_q>0$. In 1941, Duffin and Schaeffer proposed a simple criterion to decide when almost all real numbers (in the Lebesgue sense) admit an infinite number of reduced rational approximations $a/q$, $q\in S$, within distance $\Delta_q$. In this talk, I will present recent joint work with James Maynard that settles this conjecture.

MC 5417