Diophantine approximation of pi

Speaker: Dr. Pat McCarthy (NUI Maynooth)

Time: 3:00PM
Date: Wed 13th April 2011

Location: Mathematical Sciences Seminar Room

Diophantine Approximation (in one dimension) is concerned with how well we can approximate a real number α with a rational number. Specifically, suppose that ?(x)>0 and ?(x)/x tends to 0 as x decreases to 0. Can we find infinitely many fractions p/q such that


We present some results which hold for arbitrary irrational α and arbitrary algebraic α. Finally we discuss the current state of knowledge regarding the case where α=π.(This talk is part of the K-Theory, Quadratic Forms and Number Theory series.)