Ethan Lee

Investigations into the Mertens function

The Mertens function M(x) sums \mu(n) for n \leq x, where \mu is the Moebius function. Historically, it is studied because of it's connection to the Riemann hypothesis. In this talk, I will introduce the Mertens conjecture, and several proven bounds for M(x). In particular, there has been a recent burst of interest into refining bounds for M(x), and I describe my contributions to this literature using tools from complex analysis.